For a complete list with selected publications, please see below.
[32] E. Abreu, J. C. Valencia-Guevara, M. Huacasi-Machaca & J. Pérez. A numerical scheme for doubly nonlocal conservation law, CALCOLO, Volume 61 (2024). LINK: https://link.springer.com/article/10.1007/s10092-024-00624-x. Keywords: Fractional conservation laws · Doubly nonlinear nonlocal flux; Riesz potential; Hilbert transform; Numerical algorithm for the Riesz fractional Laplacian; Nonlocal Lagrangian–Eulerian scheme; Nonlocal no-flow curves.
[31] Eduardo Abreu, Richard de la Cruz, Juan Juajibioy, Wanderson Jose Lambert. Semi-discrete Lagrangian–Eulerian approach based on the weak asymptotic method for nonlocal conservation laws in several dimensions, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Volume 458 (2025). LINK: https://doi.org/10.1016/j.cam.2024.116325. Keywords: Multi-dimensional nonlocal conservation laws; Weak asymptotic method; Nonlocal no-flow curves; Semi-discrete scheme; Lagrangian–Eulerian approach.
[30] E. Abreu, M. Huacasi-Machaca, J. Pérez and J. C. Valencia-Guevara, Blowing up and dissipation for a couple of one-dimensional non-local conservation laws, to appear in New Tools in Mathematical Analysis and Applications - Proceedings of the 14th International Society for Analysis, its Applications and Computation July 17 to July 21, 2023 (ISAAC - http://www.isaacmath.org/event/conference/) Congress 2023, Ribeirão Preto, Brazil (https://dcm.ffclrp.usp.br/isaac/)”. This publication is expected to be available later on in a volume published by Springer in the Birkhäuser book series Research perspective. For those interested readers, a preprint version is fully available for download here: preprint download link.
[29] Eduardo Abreu, Eduardo Cuesta, Angel Durán and Wanderson Jose Lambert. Mathematical properties and numerical approximation of pseudo-parabolic systems, COMPUTER & MATEHMATICS WITH APLICATIONS, Volume 165 (2024). LINK: https://doi.org/10.1016/j.camwa.2024.04.015. Keywords: Pseudo-parabolic equations; Spectral methods; Error estimates; Strong stability preserving methods; Non-regular data.
[28] Eduardo Abreu, Vítor Matos, John Perez and Panters Rodriguez-Bermudez. Riemann problem solutions for a balance law under Dirac-Delta source with a discontinuous flux, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS (2024) (JHDE; https://www.worldscientific.com/doi/10.1142/S0219891624500012). Keywords: Conservation laws; Discontinuous flux; δ-Dirac; Uniqueness of weak entropy solutions; Non viscous solutions; No-flow Lagrangian-Eulerian approach.
[27] Eduardo Abreu, Wanderson Jose Lambert, Arthur Miranda do Espírito Santo and John Perez. A relaxation approach to modeling properties of hyperbolic-parabolic type models, COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, Volume 133 (2024). LINK: https://doi.org/10.1016/j.cnsns.2024.107967. Keywords: Modeling using PDEs via Relaxation; Liu sub-characteristic condition; Convection-diffusion problems; Discontinuous flux function; Discontinuous coefficient in space; Numerical validation of models.
[26] Eduardo Abreu, Jorge Agudelo, John Pérez. A triangle-based positive semi-discrete Lagrangian–Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Volume 437 (2024). LINK: https://doi.org/10.1016/j.cam.2023.115465. Keywords: Hyperbolic conservation laws, Lagrangian–Eulerian method, Semi-discrete scheme on triangular grids, Weak asymptotic analysis, Kruzhkov entropy solution, Positivity principle.
[25] Eduardo Abreu, Paola Ferraz, Wanderson José Lambert. A study of non-equilibrium wave groups in two-phase flow in high-contrast porous media with relative permeability hysteresis, COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, (2023). LINK: https://doi.org/10.1016/j.cnsns.2023.107552. Keywords: Two-phase flow; Relaxation hysteresis; Porous media; Analytical-numerical methods.
[24] Isamara Landim, Marcio A. Murad, Patricia Pereira, Eduardo Abreu. A new computational model for karst conduit flow in carbonate reservoirs including dissolution-collapse breccias, COMPUTATIONAL GEOSCIENCES, (2023). LINK: https://doi.org/10.1007/s10596-023-10229-y. Keywords: Carbonates with karst cave conduits, Lower-dimensional model reduction, Collapse-breccia, Coupled 3D/1D flows, Non-linear Robin transmission condition, Hybridized mixed methods.
[23] Julio C. Valencia-Guevara, John Pérez, Eduardo Abreu. On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Volume 528, Issue 2 (2023). LINK: https://doi.org/10.1016/j.jmaa.2023.127602. Keywords: Blow-up Keller–Segel, Multispecies chemotaxis, JKO scheme Optimal transport, Wasserstein gradient flows, Multistep discretization, Numerical simulations.
[22] Eduardo Abreu, Jorge Eliécer Agudelo, Wanderson José Lambert and John Pérez. A Lagrangian-Eulerian Method on Regular Triangular Grids for Hyperbolic Problems: Error Estimates for the Scalar Case and a Positive Principle for Multidimensional Systems, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, v.online, p.1 - 66 (26 June 26, 2023). LINK: https://doi.org/10.1007/s10884-023-10283-1. Keywords: Conservation laws and first-order hyperbolic system, no-flow curves and triangular grids, vector fields with bounded directional variation, positive Lagrangian-Eulerian method, entropy measure-valued solutions and entropy process, a priori error estimates.
[21] Eduardo Abreu and João B. Florindo. A pseudo-parabolic diffusion model to enhance deep neural texture features. MULTIMEDIA TOOLS AND APPLICATIONS, v.online, p.1 - 22 (June 29, 2023). LINK: https://doi.org/10.1007/s11042-023-15886-w. Keywords: Texture recognition, Partial Differential Equation (PDE), Convolutional neural networks, Image descriptors, PDE image/texture process.
[20] Eduardo Abreu, Arthur Espírito Santo, Wanderson Lambert, Jonh Pérez. Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian-Eulerian scheme via weak asymptotic analysis for hyperbolic problems. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, v. online, p. 47 pages (May, 2023) LINK: https://doi.org/10.1002/num.22972 Keywords: Fully discrete Lagrangian–Eulerian scheme, Kruzhkov entropy condition, maximum principle, no-flow curves, positivity-preserving, total variation nonincreasing, weak asymptotic analysis, weak bounded variation.
[19] Eduardo Abreu, Elena Bachini, John Pérez, Mario Putti. A geometrically intrinsic lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data. APPLIED MATHEMATICS AND COMPUTATION, v. 443, p. 127776 (April 15, 2023) LINK: https://doi.org/10.1016/j.amc.2022.127776 Keywords: Balance laws on surface, Shallow water equations, Non-autonomous fluxes, Spatially variable topography, Intrinsic lagrangian-Eulerian scheme, No-flow surfaces.
[18] Luis Hernandez, David Pardo, Eduardo Abreu, Judit Muñoz-Matute Ciro Díaz, Juan Galvis. An exponential integration generalized multiscale finite element method for parabolic problems. JOURNAL OF COMPUTATIONAL PHYSICS, v. online, p. 112014-21 (April 15, 2023) LINK: https://doi.org/10.1016/j.jcp.2023.112014 Keywords: Multiscale approximation, Time integration, Functions of matrices, Finite element methods.
[17] Eduardo Abreu, Paola Ferraz, Arthur Espírito Santo, Felipe Pereira, L. Santos, Fabrício Sousa. Recursive formulation and parallel implementation of multiscale mixed methods. JOURNAL OF COMPUTATIONAL PHYSICS, v. 473, p. 111681 (January 15, 2023) LINK: https://doi.org/10.1016/j.jcp.2022.111681 Keywords: Recursive Multiscale Robin Coupled Method, Parallelization ,Mixed finite elements, Domain decomposition, Fluid dynamics in porous media, Darcy's law.
[16] Jardel Vieira, Eduardo Abreu and João B. Florindo, Texture image classification based on a pseudo-parabolic diffusion model. MULTIMEDIA TOOLS AND APPLICATIONS (July 13, 2022)
LINK https://link.springer.com/article/10.1007/s11042-022-12048-2 Keywords:
Pseudo-parabolic equation, Texture recognition, Image classification, Numerical approximation methods for PDEs.
[15] Eduardo Abreu, Richard A. De la Cruz Guerrero, Juan Carlos Juajibioy Otero and Wanderson José Lambert, Lagrangian-Eulerian approach for nonlocal conservation laws. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (July 25, 2022)
LINK https://link.springer.com/article/10.1007/s10884-022-10193-8 Keywords:
Nonlocal conservation laws, Lagrangian-Eulerian approach, No-flow curves, Kruzhkov entropy solution, Applications.
[14] Eduardo Abreu, Lucas C. F. Ferreira, Juan G. G. Delgado and John
Pérez, On a 1D model with nonlocal interactions and mass
concentrations: an analytical-numerical approach. NONLINEARITY, v.35 (2022)
p.1734 - 1772. LINK https://iopscience.iop.org/article/10.1088/1361-6544/ac5097 Keywords:
Nonlinear transport equation, Measure initial data, Nonlocal flow, Blow-up;
Asymptotic behavior, Finite-time mass concentration, Analytical and
computational methods.
[13] Eduardo Abreu, Jean François, Wanderson Lambert and John
Pérez, A semi-discrete Lagrangian-Eulerian scheme for
hyperbolic-transport models. JOURNAL OF COMPUTATIONAL AND APPLIED
MATHEMATICS, v.406 (2022), p.114011. LINK https://www.sciencedirect.com/science/article/abs/pii/S0377042721005963 Keywords:
Hyperbolic conservation laws, Semi-discrete scheme, Blow-up analysis, Weak
asymptotic analysis, Total variation nonincreasing, Kruzhkov entropy solution.
[12] Eduardo Abreu, Jean François, Wanderson Lambert and John
Pérez, A Class of Positive Semi-discrete Lagrangian-Eulerian Schemes
for Multidimensional Systems of Hyperbolic Conservation Laws. JOURNAL OF
SCIENTIFIC COMPUTING, v.90 (2022), p.40 (79 pages). LINK https://link.springer.com/article/10.1007/s10915-021-01712-8 Keywords:
Hyperbolic conservation laws, Semidiscrete Lagrangian-Eulerian schemes,
Positivity principle - Systems of Hyperbolic Conse, Weak asymptotic analysis,
Total variation nonincreasing (TVNI).
[11] Jardel Vieira, Eduardo Abreu and João B. Florindo, Texture
image classification based on a pseudo-parabolic diffusion model. To Appear
in MULTIMEDIA TOOLS AND APPLICATIONS (2022) 22 pages. (Arxiv LINK https://arxiv.org/pdf/2011.07173) Keywords:
Texture image classification, Pseudo-parabolic diffusion process, Local
descriptor, Image Analysis.
[10] Eduardo Abreu and Angél M. Durán, Spectral discretizations
analysis with time strong stability preserving properties for pseudo-parabolic
models. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.102 (2021), p.15 -
44. LINK https://doi.org/10.1016/j.camwa.2021.10.001 Keywords:
pseudo-parabolic equations, Spectral methods, error estimates, strong stability
preserving methods, non-regular data.
[9] Paola Ferraz, Patricia Pereira, Eduardo Abreu and Marcio
Murad, Recursive Mixed Multiscale Model Reduction for Karst
Conduit-Flow in Carbonate Reservoirs. TRANSPORT IN POROUS MEDIA. v.139
(2021) p. 527 - 558. LINK: https://link.springer.com/article/10.1007/s11242-021-01678-z Keywords:
Karst conduits, lower-dimensional model reduction, Homogenization, coupled
1D/3D flows, multiscale mixed finite element.
[8] Eduardo Abreu, Vitor Matos, John Pérez and Panters
Bermudez-Rodriguez, A Class of Lagrangian-Eulerian Shock-Capturing
Schemes for First-Order Hyperbolic Problems with Forcing Terms. JOURNAL OF
SCIENTIFIC COMPUTING, v.86 (2021) p.14 (47 pages). LINK: https://doi.org/10.1007/s10915-020-01392-w Keywords:
Hyperbolic Balance Laws, Hyperbolic conservation laws, Lagrangian-Eulerian
method, 4 by 4 (2D) Compressible Euler Flows, 3 by (2D) Shallow-Water
Equations, Multidimensional Hyperbolic Sytems of Conservation.
[7] Eduardo Abreu, Richard Guerrero and Wanderson Lambert, Riemann
problems and delta-shock solutions for a Keyfitz-Kranzer system with a forcing
term. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.502 (2021) p.15
– 125267. LINK: https://doi.org/10.1016/j.jmaa.2021.125267 Keywords:
Nonsymmetric Keyfitz-Kranzer system, Improved Lagragian-Eulerian scheme,
Coulomb friction term, Delta-shock solutions, Riemann problem, Source terms.
[6] Eduardo Abreu, Richard Guerraro and Marcelo M. Santos, Interaction
of delta shock waves for a nonsymmetric Keyfitz-Kranzer system of conservation
laws. MONATSHEFTE FUR MATHEMATIK, v.194, (2021) p.737 – 766. LINK: https://link.springer.com/article/10.1007%2Fs00605-021-01524-w Keywords:
Delta shock waves, System of conservation laws, Nonsymmetric Keyfitz-Kranzer
system, Lagrangian-Eulerian method.
[5] Eduardo Abreu and João B. Florindo, A Study on a Feedforward
Neural Network to Solve Partial Differential Equations in Hyperbolic-Transport
Problems In: Lecture Notes in Computer Science.31 ed.: Springer
International Publishing (2021) p. 398-411. LINK: https://link.springer.com/10.1007/978-3-030-77964-1_31 Keywords:
Neural network, Partial differential equation, Transport models, Numerical
approximation methods for PDEs, pproximation of entropy solutions.
[4] Eduardo Abreu and João B. Florindo, An Application of a
Pseudo-Parabolic Modeling to Texture Image Recognition In: Lecture
Notes in Computer Science.31 ed.: Springer International Publishing, 2021, p.
386-397. LINK: https://link.springer.com/10.1007/978-3-030-77964-1_30 Keywords:
Pseudo-parabolic equation, Texture recognition, Image classification, Computational
Methods for PDEs.
[3] Julia S. S. Borges, José A. M. Ferreira, Giuseppe Romanazzi,
Eduardo Abreu, Drug release from viscoelastic polymeric matrices - a
stable and supraconvergent FDM , MATHEMATICS WITH APPLICATIONS, v.99
(2021), p.257 – 269. LINK: https://doi.org/10.1016/j.camwa.2021.08.007 Keywords:
Drug Release, viscoelastic polymeric matrix, Dissolved drug transport, Finite
Difference Method (FDM), Stability and supraconvergent FDM, Dissolution.
[2] Eduardo Abreu, Ciro Díaz, Juan Galvis, John Pérez, On the
Conservation Properties in Multiple Scale Coupling and Simulation for Darcy
Flow with Hyperbolic-Transport in Complex Flows. MULTISCALE MODELING &
SIMULATION, v.18 (2020) p.1375 – 1408. LINK: https://epubs.siam.org/doi/10.1137/20M1320250 Keywords:
Multiscale Modeling and Simulation, Hyperbolic conservation laws, High order
conservative finite element formulation, Darcy flow, Elliptic-Poisson problem,
Multiscale Complex Flows.
[1] Eduardo Abreu; Paola Ferraz and Jardel Vieira, Numerical
resolution of a pseudo-parabolic Buckley-Leverett model with gravity and
dynamic capillary pressure in heterogeneous porous media. JOURNAL OF
COMPUTATIONAL PHYSICS, v.411 (2020), p.109395 – (24 pages). LINK: https://doi.org/10.1016/j.jcp.2020.109395 Keywords: Dynamic
capillary pressure, Two-phase flow, pseudo-parabolic PDE, Finite volume, Finite
element method, Porous media flows.
[64] E. Abreu, J. C. Valencia-Guevara, M. Huacasi-Machaca & J. Pérez. A numerical scheme for doubly nonlocal conservation law, CALCOLO, Volume 61 (2024). LINK: https://link.springer.com/article/10.1007/s10092-024-00624-x. Keywords: Fractional conservation laws · Doubly nonlinear nonlocal flux; Riesz potential; Hilbert transform; Numerical algorithm for the Riesz fractional Laplacian; Nonlocal Lagrangian–Eulerian scheme; Nonlocal no-flow curves.
[63] Eduardo Abreu, Richard de la Cruz, Juan Juajibioy, Wanderson Jose Lambert. Semi-discrete Lagrangian–Eulerian approach based on the weak asymptotic method for nonlocal conservation laws in several dimensions, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Volume 458 (2025). LINK: https://doi.org/10.1016/j.cam.2024.116325. Keywords: Multi-dimensional nonlocal conservation laws; Weak asymptotic method; Nonlocal no-flow curves; Semi-discrete scheme; Lagrangian–Eulerian approach.
[62] E. Abreu, M. Huacasi-Machaca, J. Pérez and J. C. Valencia-Guevara, Blowing up and dissipation for a couple of one-dimensional non-local conservation laws, to appear in New Tools in Mathematical Analysis and Applications - Proceedings of the 14th International Society for Analysis, its Applications and Computation July 17 to July 21, 2023 (ISAAC - http://www.isaacmath.org/event/conference/) Congress 2023, Ribeirão Preto, Brazil (https://dcm.ffclrp.usp.br/isaac/)”. This publication is expected to be available later on in a volume published by Springer in the Birkhäuser book series Research perspective. For those interested readers, a preprint version is fully available for download here: preprint download link.
[61] Eduardo Abreu, Eduardo Cuesta, Angel Durán and Wanderson Jose Lambert. Mathematical properties and numerical approximation of pseudo-parabolic systems, COMPUTER & MATEHMATICS WITH APLICATIONS, Volume 165 (2024). LINK: https://doi.org/10.1016/j.camwa.2024.04.015. Keywords: Pseudo-parabolic equations; Spectral methods; Error estimates; Strong stability preserving methods; Non-regular data.
[60] Eduardo Abreu, Vítor Matos, John Perez and Panters Rodriguez-Bermudez. Riemann problem solutions for a balance law under Dirac-Delta source with a discontinuous flux, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS (2024) (JHDE; https://www.worldscientific.com/worldscinet/jhde). Keywords: Conservation laws; Discontinuous flux; δ-Dirac; Uniqueness of weak entropy solutions; Non viscous solutions; No-flow Lagrangian-Eulerian approach.
[59] Eduardo Abreu, Wanderson Jose Lambert, Arthur Miranda do Espírito Santo and John Perez. A relaxation approach to modeling properties of hyperbolic-parabolic type models, COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, Volume 133 (2024). LINK: https://doi.org/10.1016/j.cnsns.2024.107967. Keywords: Modeling using PDEs via Relaxation; Liu sub-characteristic condition; Convection-diffusion problems; Discontinuous flux function; Discontinuous coefficient in space; Numerical validation of models.
[58] Eduardo Abreu, Jorge Agudelo, John Pérez. A triangle-based positive semi-discrete Lagrangian–Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Volume 437 (2024). LINK: https://doi.org/10.1016/j.cam.2023.115465. Keywords: Hyperbolic conservation laws, Lagrangian–Eulerian method, Semi-discrete scheme on triangular grids, Weak asymptotic analysis, Kruzhkov entropy solution, Positivity principle.
[57] Eduardo Abreu, Paola Ferraz, Wanderson José Lambert. A study of non-equilibrium wave groups in two-phase flow in high-contrast porous media with relative permeability hysteresis, COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, (2023). LINK: https://doi.org/10.1016/j.cnsns.2023.107552. Keywords: Two-phase flow; Relaxation hysteresis; Porous media; Analytical-numerical methods.
[56] Isamara Landim, Marcio A. Murad, Patricia Pereira, Eduardo Abreu. A new computational model for karst conduit flow in carbonate reservoirs including dissolution-collapse breccias, COMPUTATIONAL GEOSCIENCES, (2023). LINK: https://doi.org/10.1007/s10596-023-10229-y. Keywords: Carbonates with karst cave conduits, Lower-dimensional model reduction, Collapse-breccia, Coupled 3D/1D flows, Non-linear Robin transmission condition, Hybridized mixed methods.
[55] Eduardo Abreu, Jorge Agudelo, John Pérez. A triangle-based positive semi-discrete Lagrangian–Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Volume 437 (2024). LINK: https://doi.org/10.1016/j.cam.2023.115465. Keywords: Hyperbolic conservation laws, Lagrangian–Eulerian method, Semi-discrete scheme on triangular grids, Weak asymptotic analysis, Kruzhkov entropy solution, Positivity principle.
[54] Julio C. Valencia-Guevara, John Pérez, Eduardo Abreu. On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Volume 528, Issue 2 (2023). LINK: https://doi.org/10.1016/j.jmaa.2023.127602. Keywords: Blow-up Keller–Segel, Multispecies chemotaxis, JKO scheme Optimal transport, Wasserstein gradient flows, Multistep discretization, Numerical simulations.
[53] Eduardo Abreu, Jorge Eliécer Agudelo, Wanderson José Lambert and John Pérez. A Lagrangian-Eulerian Method on Regular Triangular Grids for Hyperbolic Problems: Error Estimates for the Scalar Case and a Positive Principle for Multidimensional Systems, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, v.online, p.1 - 66 (26 June 26, 2023). LINK: https://doi.org/10.1007/s10884-023-10283-1. keywords: Conservation laws and first-order hyperbolic system, no-flow curves and triangular grids, vector fields with bounded directional variation, positive Lagrangian-Eulerian method, entropy measure-valued solutions and entropy process, a priori error estimates.
[52] Eduardo Abreu and João B. Florindo. A pseudo-parabolic diffusion model to enhance deep neural texture features. MULTIMEDIA TOOLS AND APPLICATIONS, v.online, p.1 - 22 (June 29, 2023). LINK: https://doi.org/10.1007/s11042-023-15886-w. keywords: Texture recognition, Partial Differential Equation (PDE), Convolutional neural networks, Image descriptors, PDE image/texture process.
[51] Eduardo Abreu, Arthur Espírito Santo, Wanderson Lambert, Jonh Pérez. Convergence,
bounded variation properties and Kruzhkov solution of a fully discrete
Lagrangian-Eulerian scheme via weak asymptotic analysis for hyperbolic
problems. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, v. online, p. 47 pages (May, 2023) LINK: https://doi.org/10.1002/num.22972 Keywords: Fully
discrete Lagrangian–Eulerian scheme, Kruzhkov entropy condition,
maximum principle, no-flow curves, positivity-preserving, total
variation nonincreasing, weak asymptotic analysis, weak bounded
variation.
[50] Eduardo Abreu, Elena Bachini, John Pérez, Mario Putti. A
geometrically intrinsic lagrangian-Eulerian scheme for 2D shallow water
equations with variable topography and discontinuous data. APPLIED MATHEMATICS AND COMPUTATION, v. 443, p. 127776 (April 15, 2023) LINK: https://doi.org/10.1016/j.amc.2022.127776 Keywords:
Balance laws on surface, Shallow water equations, Non-autonomous
fluxes, Spatially variable topography, Intrinsic lagrangian-Eulerian
scheme, No-flow surfaces.
[49] Luis Hernandez, David Pardo, Eduardo Abreu, Judit Muñoz-Matute Ciro Díaz, Juan Galvis. An exponential integration generalized multiscale finite element method for parabolic problems. JOURNAL OF COMPUTATIONAL PHYSICS, v. online, p. 112014-21 (April 15, 2023) LINK: https://doi.org/10.1016/j.jcp.2023.112014 Keywords: Multiscale approximation, Time integration, Functions of matrices, Finite element methods.
[48] Eduardo Abreu, Paola Ferraz, Arthur Espírito Santo, Felipe Pereira, L. Santos, Fabrício Sousa. Recursive formulation and parallel implementation of multiscale mixed methods. JOURNAL OF COMPUTATIONAL PHYSICS, v. 473, p. 111681 (January 15, 2023) LINK: https://doi.org/10.1016/j.jcp.2022.111681 Keywords:
Recursive Multiscale Robin Coupled Method, Parallelization ,Mixed
finite elements, Domain decomposition, Fluid dynamics in porous media,
Darcy's law.
[47] Jardel Vieira, Eduardo Abreu and João B. Florindo, Texture image classification based on a pseudo-parabolic diffusion model. MULTIMEDIA TOOLS AND APPLICATIONS (July 13, 2022)
LINK https://link.springer.com/article/10.1007/s11042-022-12048-2 Keywords:
Pseudo-parabolic equation, Texture recognition, Image classification, Numerical approximation methods for PDEs.
[45] Eduardo Abreu, Lucas C. F. Ferreira, Juan G. G. Delgado, John
Pérez (2022), On a 1D model with nonlocal interactions and
mass concentrations: an analytical-numerical approach. NONLINEARITY, v.35,
p.1734 – 1772. LINK https://iopscience.iop.org/article/10.1088/1361-6544/ac5097 Keywords:
Nonlinear transport equation, Measure initial data, Nonlocal flow, Blow-up;
Asymptotic behavior, Finite-time mass con- centration, Analytical and
computational methods.
[44] Eduardo Abreu, Jean François, Wanderson Lambert and John Pérez (2022), A
semi-discrete Lagrangian-Eulerian scheme for hyperbolic-transport models.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.406, p.114011. LINK https://www.sciencedirect.com/science/article/abs/pii/S0377042721005963 Keywords: Hyperbolic
conservation laws, Semi-discrete scheme, Blow-up analysis, Weak asymptotic
analysis, Total variation nonincreasing, Kruzhkov entropy solution.
[43] Eduardo Abreu, Jean François, Wanderson Lambert and John
Pérez (2022), A Class of Positive Semi-discrete
Lagrangian-Eulerian Schemes for Multidimensional Systems of Hyperbolic
Conservation Laws. JOURNAL OF SCIENTIFIC COMPUTING, v.90 p.40
(79 pages). LINK https://link.springer.com/article/10.1007/s10915-021-01712-8 Keywords:
Hyperbolic conservation laws, Semidiscrete Lagrangian-Eulerian schemes,
Positivity principle - Systems of Hyperbolic Conse, Weak asymptotic analysis,
Total variation nonincreasing (TVNI).
[42] Jardel Vieira, Eduardo Abreu and João B.
Florindo, Texture image classification based on a pseudo-parabolic
diffusion model (2022). To Appear in MULTIMEDIA TOOLS AND
APPLICATIONS, 22 pages. (Arxiv LINK https://arxiv.org/pdf/2011.07173) Keywords:
Texture image classification, Pseudo-parabolic diffusion process, Local
descriptor, Image Analysis.
[41] Eduardo Abreu and Angél M. Durán (2021), Spectral
discretizations analysis with time strong stability preserving properties for
pseudo-parabolic models. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.102
p.15 - 44. LINK https://doi.org/10.1016/j.camwa.2021.10.001 Keywords: pseudo-parabolic
equations, Spectral methods, error estimates, strong stability preserving
methods, non-regular data.
[40] Paola Ferraz, Patricia Pereira, Eduardo Abreu and
Marcio Murad (2021) , Recursive Mixed Multiscale Model
Reduction for Karst Conduit-Flow in Carbonate Reservoirs. TRANSPORT IN
POROUS MEDIA. , v.139, p. 527 - 558. LINK: https://link.springer.com/article/10.1007/s11242-021-01678-z Keywords:
Karst conduits, lower-dimensional model reduction, Homogenization, coupled
1D/3D flows, multiscale mixed finite element.
[39] Eduardo Abreu, Vitor Matos, John Pérez and Panters
Bermudez-Rodriguez (2021) , A Class of Lagrangian-Eulerian
Shock-Capturing Schemes for First-Order Hyperbolic Problems with Forcing Terms.
JOURNAL OF SCIENTIFIC COMPUTING, v.86,p.14 (47 pages). LINK: https://doi.org/10.1007/s10915-020-01392-w Keywords:
Hyperbolic Balance Laws, Hyperbolic conservation laws, Lagrangian-Eulerian
method, 4 by 4 (2D) Compressible Euler Flows, 3 by (2D) Shallow-Water
Equations, Multidimensional Hyperbolic Sytems of Conservation.
[38] Eduardo Abreu, Richard Guerrero and Wanderson
Lambert, Riemann problems and delta-shock solutions for a
Keyfitz-Kranzer system with a forcing term. JOURNAL OF MATHEMATICAL
ANALYSIS AND APPLICATIONS, v.502 (2021) p.15 – 125267. LINK: https://doi.org/10.1016/j.jmaa.2021.125267 Keywords:
Nonsymmetric Keyfitz-Kranzer system, Improved Lagragian-Eulerian scheme,
Coulomb friction term, Delta-shock solutions, Riemann problem, Source terms.
[37] Eduardo Abreu, Richard Guerraro and Marcelo M.
Santos (2021), Interaction of delta shock waves for a
nonsymmetric Keyfitz-Kranzer system of conservation laws. MONATSHEFTE FUR
MATHEMATIK, v.194, p.737 – 766. LINK: https://link.springer.com/article/10.1007%2Fs00605-021-01524-w Keywords:
Delta shock waves, System of conservation laws, Nonsymmetric Keyfitz-Kranzer
system, Lagrangian-Eulerian method.
[36] Eduardo Abreu and João B. Florindo (2021), A Study
on a Feedforward Neural Network to Solve Partial Differential Equations in
Hyperbolic-Transport Problems In: Lecture Notes in Computer Science.31
ed.: Springer International Publishing p. 398-411. LINK: https://link.springer.com/10.1007/978-3-030-77964-1_31 Keywords:
Neural network, Partial differential equation, Transport models, Numerical
approximation methods for PDEs, pproximation of entropy solutions.
[35] Eduardo Abreu and João B. Florindo (2021), An
Application of a Pseudo-Parabolic Modeling to Texture Image Recognition In:
Lecture Notes in Computer Science.31 ed.: Springer International Publishing, p.
386-397. LINK: https://link.springer.com/10.1007/978-3-030-77964-1_30 Keywords:
Pseudo-parabolic equation, Texture recognition, Image classification,
Computational Methods for PDEs.
[34] Julia S. S. Borges, José A. M. Ferreira, Giuseppe
Romanazzi and Eduardo Abreu (2021), Drug release from
viscoelastic polymeric matrices - a stable and supraconvergent FDM ,
MATHEMATICS WITH APPLICATIONS, v.99, p.257 – 269. LINK: https://doi.org/10.1016/j.camwa.2021.08.007 Keywords:
Drug Release, viscoelastic polymeric matrix, Dissolved drug transport, Finite
Difference Method (FDM), Stability and supraconvergent FDM, Dissolution.
[33] Eduardo Abreu, Ciro Díaz, Juan Galvis and John Pérez (2020), On
the Conservation Properties in Multiple Scale Coupling and Simulation for Darcy
Flow with Hyperbolic-Transport in Complex Flows. MULTISCALE MODELING &
SIMULATION, v.18, p.1375 – 1408. LINK: https://epubs.siam.org/doi/10.1137/20M1320250 Keywords:
Multiscale Modeling and Simulation, Hyperbolic conservation laws, High order
conservative finite element formulation, Darcy flow, Elliptic-Poisson problem,
Multiscale Complex Flows.
[32] Eduardo Abreu; Paola Ferraz and Jardel Vieira (2020),
Numerical resolution of a pseudo-parabolic Buckley-Leverett model with
gravity and dynamic capillary pressure in heterogeneous porous media.
JOURNAL OF COMPUTATIONAL PHYSICS, v.411, p.109395 – (24 pages). LINK: https://doi.org/10.1016/j.jcp.2020.109395 Keywords: Dynamic
capillary pressure, Two-phase flow, pseudo-parabolic PDE, Finite volume, Finite
element method, Porous media flows.
[31] Eduardo Abreu, Ciro Díaz and Juan Galvis (2019), A
convergence analysis of Generalized Multiscale Finite Element Methods.
JOURNAL OF COMPUTATIONAL PHYSICS. , v.396, p.303 – 324. LINK: https://doi.org/10.1016/j.jcp.2019.06.072 Keywords:
multiscale elliptic PDE problems, GMsFEM spaces, regularity numerical analysis
tool.
[30] Eduardo Abreu, Abel Bustos, Paola Ferraz and Wanderson
Lambert (2019), A Relaxation Projection Analytical-Numerical
Approach in Hysteretic Two-Phase Flows in Porous Media. JOURNAL OF
SCIENTIFIC COMPUTING. , v.79, p.1936. LINK: https://link.springer.com/article/10.1007%2Fs10915-019-00923-4 Keywords:
Relaxation, Hyperbolic conservation laws, Riemann problem, Projection method,
Hysteretic two-phase flow, Finite volume/element.
[29] Eduardo Abreu and John Pérez (2019), A fast,
robust, and simple Lagrangian-Eulerian solver for balance laws and applications.
COMPUTERS & MATHEMATICS WITH APPLICATIONS. , v.77, p.2310 –
2336. LINK: https://www.sciencedirect.com/science/article/pii/S0898122118307119 Keywords:
Balance Laws, Conservation laws, Conservative discretizations,
Lagrangian-Eulerian Finite Volume.
[28] Luis G. C. Santos, Nelson Manzanares Filho and Eduardo
Abreu (2018), Comparing RBF-FD approximations based on
stabilized gaussians and on polyharmonic splines with polynomials.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. , v.115, p.462 –
500. LINK: https://onlinelibrary.wiley.com/doi/10.1002/nme.5813 Keywords:
RBF-FD approximations, Polyharmonic splines, RBF-FD based meshless,
Applications in science and engineering problems.
[27] Eduardo Abreu, Juan Galvis, Marcus Sarkis and Ciro
Díaz (2018), On high-order conservative finite element
methods. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.75, p.1852 –
1867. LINK: https://www.sciencedirect.com/science/article/pii/S0898122117306685 Keywords:
Conservative High-order FEM, Darcy flow, Porous media, High contrast
heterogeneity, Elliptic-Poisson problem.
[26] Eduardo Abreu; Arthur Mirand and John Pérez (2018), Lagrangian-Eulerian approximation methods for balance laws and hyperbolic conservation laws. REVISTA UIS INGENIERÍAS, v.17, p.191 – 200. LINK: http://revistas.uis.edu.co/index.php/revistauisingenierias/article/view/7662/7921 Keywords: Balance Laws, Conservation laws, Lagrangian-Eulerian method, Nonlinear transport equations.
[25] Juan Galvis, Eduardo Abreu, Ciro Díaz and Marcus
Sarkis (2018), On High-Order Approximation and Stability
with Conservative Properties In: LECTURE NOTES IN COMPUTATINAL SCIENCE
AND ENGINEERING.125 ed.: Springer International Publishing, p. 253-260.
LINK: http://link.springer.com/10.1007/978-3-319-93873-8_23 Keywords:
Elliptic PDE (Poisson's equation), Conservative High-Order Finite Element
Method, Stability.
[24] Eduardo Abreu, Mathilde Colombeau and Evgeny Yu
Panov (2017), Approximation of entropy solutions to
degenerate nonlinear parabolic equations. ZEITSCHRIFT FUR ANGEWANDTE
MATHEMATIK UND PHYSIK. , v.68, p.133. LINK https://link.springer.com/article/10.1007/s00033-017-0877-6 Keywords:
Weak asymptotic method, degenerate nonlinear parabolic equations, Approximation
of entropy solutions.
[23] Eduardo Abreu, Wanderson Lambert, John Pérez and
Arthur Miranda (2017), A new finite volume approach for
transport models and related applications with balancing source terms.
MATHEMATICS AND COMPUTERS IN SIMULATION, v.137, p.2 – 28. LINK: https://doi.org/10.1016/j.matcom.2016.12.012 Keywords:
Conservation laws, Balance Laws, Flow in Porous Media, Shallow Water Equations,
Lagrangian-Eulerian Finite Volume, Classical and non-classical solutions of
PDEs.
[22] Eduardo Abreu and Jardel Vieira (2017), Computing
numerical solutions of the pseudo-parabolic Buckley-Leverett equation with
dynamic capillary pressure. MATHEMATICS AND COMPUTERS IN SIMULATION, v.137,
p.29 – 48. LINK: https://doi.org/10.1016/j.matcom.2016.10.006 Keywords:
Pseudo-parabolic PDE, Dynamic capillary pressure, Two-phase flow, Mixed hybrid
finite volume-element method, Flow in Porous Media.
[21] Eduardo Abreu, Mathilde Colombeau and Evgeny Yu
Panov (2016), Weak asymptotic methods for
scalar equations and systems. JOURNAL OF MATHEMATICAL ANALYSIS AND
APPLICATIONS, v.444(2), p.1203 - 1232, 2016. LINK: https://doi.org/10.1016/j.jmaa.2016.06.047 Keywords:
Weak asymptotic methods, approximate solutions for first-order
hyperbolic equations, generalized solutions, discontinuous nonlinearity and
systems having irregular solutions.
[20] Eduardo Abreu, Abel Alvarez Bustos and Wanderson
Lambert (2016), A unsplitting finite volume
method for medels with stiff relaxation source term. BULLETIN OF THE
BRAZILIAN MATHEMATICAL SOCIETY, v.47, p.5 - 20, 2016. LINK: https://link.springer.com/article/10.1007/s00574-016-0118-1 Keywords:
Asymptotic expansion, Balance Laws, Finite volume.
[19] Eduardo Abreu, Pablo Castaneda, Fred Furtado and Dan
Marchesin (2016), On a universal structure for immiscible
three-phase flow in virgin reservoirs. COMPUTATIONAL GEOSCIENCES, v.20,
p.171 - 185, 2016. LINK: https://link.springer.com/article/10.1007/s10596-016-9556-5 Keywords:
Riemann problem, Three-phase flow, Conservation laws, Modeling and simulation
of multi-scale phenomena.
[18] Eduardo Abreu, Abel Alvarez Bustos, Wanderson Lambert
(2015), Non-monotonic traveling wave and computational solutions for
gas dynamics Euler equations with stiff relaxation source terms. COMPUTERS
& MATHEMATICS WITH APPLICATIONS, v.70, p.2155 - 2176, 2015.
LINK: https://doi.org/10.1016/j.camwa.2015.07.002 Keywords: Non-monotonic
traveling wave, Euler equations, Friction & Gravity, Asymptotic expansion,
Central finite volume.
[17] Eduardo Abreu, Abel Alvarez Bustos, Paola Ferraz and
Wanderson Lambert (2015), A computational multiscale approach for
incompressible two-phase flow in heterogeneous porous media including relative
permeability hysteresis In: MAMERN VI–2015 - 6th International Conference
on Approximation Methods and Numerical Modelling in Environment and Natural
Resources, Conf. Site http://mamern15.sciencesconf.org/, Pau/France.
Proceedings of the 6th International Conference on Approximation Methods and
Numerical Modelling in Environment and Natural Resources Pau. Gráficas La
Madraza. Albolote.: Editorial Universidad de Granada, 2015. v.1. p.349 –
366. Keywords: Conservation laws, Riemann problem, Hysteresis,
Flow in Porous Media.
[16] Eduardo Abreu, Wanderson Lambert, Athur Mirand and
John Pérez (2015), A Lagrangian-Eulerian algorithm for solving
hyperbolic conservation laws with applications In: MAMERN VI–2015 - 6th
International Conference on Approximation Methods and Numerical Modelling in
Environment and Natural Resources, Conf. ite http://mamern15.sciencesconf.org/, Pau/France.
Proceedings of the 6th International Conference on Approximation Methods and
Numerical Modelling in Environment and Natural Resources Pau. Gráficas La
Madraza. Albolote.: Editorial Universidad de Granada, 2015. v.1. p.599 –
618. Keywords: Conservation laws, Balance Laws, Lagrangian-Eulerian
method, Fluid Dynamics, Flow in Porous Media.
[15] Eduardo Abreu and Jardel Vieira (2015), A
mixed hybrid finite element/volume approach for a pseudo-parabolic linked to
two-phase flow in porous media with dynamic effects in the capillary pressure,
In: MAMERN VI–2015 - 6th International Conference on Approximation Methods and
Numerical Modelling in Environment and Natural Resources,, Conf. Site http://mamern15.sciencesconf.org/,
Pau/France. Proceedings of the 6th International Conference on
Approximation Methods and Numerical Modelling in Environment and Natural
Resources Pau. Gráficas La Madraza. Albolote.: Editorial Universidad de
Granada, 2015. v.1. p.665 - 687. Keywords: Pseudo-parabolic
PDE, Dynamic capillary pressure, Mixed-Hybrid Finite Elements, Finite volume.
[14] Eduardo Abreu (2014), Numerical modelling of
three-phase immiscible flow in heterogeneous porous media with gravitational
effects. MATHEMATICS AND COMPUTERS IN SIMULATION, v.97, p.234 -
259. LINK: https://doi.org/10.1016/j.matcom.2013.09.010 Keywords:
Three-phase flow, Gravity, Discontinuous capillary pressure, spatially varying
flux functions, Mixed-Hybrid Finite Elements, convection-diffusion problem.
[13] Eduardo Abreu (2014), Numerical simulation
of wave propagation in three-phase flows in porous media with spatially varying
flux functions In: 4th International Conference on Hyperbolic Problems:
Theory, Numerics, Applications, 2014, Padova/Italy. The proceedings of HYP2012.
American Institute of Mathematical Sciences Series on Applied Mathematics,
2014. v.8. p.233 – 240 LINK: https://www.aimsciences.org/fileAIMS/cms/news/info/HYP2012_Proceedings_final_3_optimize_part1.pdf Keywords:
Hyperbolic conservation laws, spatially varying flux functions, three-phase
discontinuous capillary pressure.
[12] Eduardo Abreu, Grazione Souza and Adolfo Pires (2014),
Well-Reservoir Coupling on the Numerical Simulation of Horizontal Wells in
Gas Reservoirs In: SPE Latin America and Caribbean Petroleum Engineering
Conference, Maracaibo. SPE Latin America and Caribbean Petroleum
Engineering Conference. Society of Petroleum Engineers, 2014. v.1.
LINK: https://onepetro.org/SPELACP/proceedings-abstract/13LACP/2-13LACP/D021S018R001/210314 Keywords:
Drillstem Testing, Upstream Oil & Gas, reservoir simulation, drillstem/well
testing, Directional Drilling, Fluid Dynamics, numerical simulation, flow in
porous media, drilling operation, semi-log plot.
[11] Eduardo Abreu and Duilio Conceição (2013),
Numerical Modeling of Degenerate Equations in Porous Media Flow. Journal
of Scientific Computing, v.55, p.688 - 717, 2013. LINK: https://link.springer.com/article/10.1007/s10915-012-9653-0 Keywords: Degenerate
Parabolic System, Operator Splitting, Three-phase flow, Random porous media,
Mixed finite elements methods.
[10] Eduardo Abreu and Wandrson Lambert (2012),
Computational Modeling Technique for Numerical Simulation of Immiscible
Two-phase Flow Problems Involving Flow and Transport Phenomena in Porous Media
With Hysteresis In: 4th International Conference on Porous Media and its
Applications in Science, Engineering and Industry, 2012, Potsdam. AMERICAN
INSTITUTE OF PHYSICS (AIP) CONFERENCE PROCEEDINGS, v.1453. p.141 – 146.
LINK: https://doi.org/10.1063/1.4711166 Keywords:
Hysteresis , Porous Media, Two-phase Flow ProblemsRiemann problem, Hyperbolic
conservation laws, Flow in Porous Media.
[9] Eduardo Abreu Simone ribeiro and Felipe Pereira (2009),
Central Schemes for Porous Media Flow. COMPUTATIONAL & APPLIED
MATHEMATICS, v.28, p.87 - 110, 2009. LINK https://www.scielo.br/pdf/cam/v28n1/a05v28n1.pdf Keywords:
Central schemes for hyperbolic conservation laws, Flow in Porous Media,
Heterogeneity, Mixed finite elements methods.
[8] Eduardo Abreu; Jim Douglas Jr, Fred Furtado and Felipe
Pereira, (2009), Operator Splitting for Three-Phase Flow in
Heterogeneous Porous Media. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, p.72 -
84, 2009. LINK http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.493.7870&rep=rep1&type=pdf Keywords:
Operator Splitting, Flow in Porous Media, Modeling and simulation of
multi-scale phenomena, Mixed finite elements methods, Central Schemes,
Heterogeneity.
[7] Eduardo Abreu, Jim Douglas Jr, Fred Furtado and Felipe
Pereira (2008), Operator Splitting Based on Physics for Flow in
Porous Media. Special Issue: Additive and Multiplicative Operator Splitting.
INTERNATIONAL JOURNAL OF COMPUTATINAL SCIENCE, v.02, p.315 - 335, 2008.
LINK: https://www.researchgate.net/publication/291783051_Operator_splitting_based_on_physics_for_flow_in_porous_media Keywords: Operator
Splitting, Three-phase flow, Heterogeneous porous media, Transitional waves,
Central schemes for hyperbolic conservation laws, Mixed finite elements methods.
[6] E. Abreu, Fred Furtado, Felipe Pereira and Grazione Souza (2008),
Numerical Modeling of Two-phase Flow With Hysteresis in Heterogeneous Porous
Media. In RIO OIL & GAS CONFERENCE, IBP1685 (2008), pp. 8–15.
LINK: https://www.osti.gov/etdeweb/biblio/21150482 Keywords: Hysteresis,
Porous media, Two-phase oil-water, Conservative Numerical methods.
[5] Eduardo Abreu and Felipe Pereira (2007, in
Portuguese), Desenvolvimento de Novas Estratégias Para a Recuperação
Avançada de Hidrocarbonetos em Reservatórios de Petróleo. Boletim Técnico
da Produção de Petróleo, v.2, p.83 - 106, 2007. Keywords: Three-phase
flows, Heterogeneous porous media, Advanced hydrocarbon recovery, Operator
splitting, Mixed finite elements, Central schemes.
[4] Eduardo Abreu; Jim Douglas Jr, Fred Furtado, Dan
Marchesin and Felipe Pereira (2006), Three-Phase Immiscible
Displacement in Heterogeneous Petroleum Reservoirs. MATHMATICS AND
COMPUTERS IN SIMULATION, v.73, p.2 - 20, 2006. LINK: https://doi.org/10.1016/j.matcom.2006.06.018 Keywords: Three-phase
flow, Transitional waves, Operator Splitting, Central schemes for hyperbolic
conservation laws, Mixed finite elements methods, Modeling and simulation of
multi-scale phenomena.
[3] Eduardo Abreu, Fred Furtado and Felipe Pereira (2006),
On The Numerical Simulation of Three-phase Flows in Heterogeneous Porous
Media. Lecture Notes in Computer Science. , v.4395, p.504 – 517.
LINK: https://link.springer.com/chapter/10.1007/978-3-540-71351-7_39 Keywords: Three-phase
flow, stability of non-classical waves, Relative permeability, Corey-type
models, non-strictly hyperbolic systems of conservation laws.
[2] Eduardo Abreu; Fred Furtado and Felipe Pereira (2004),
On the Numerical Simulation of Three-Phase Reservoir Transport Problems.
Transport Theory and Statistical Physics. , v.33, p.503 - 526, 2004.
LINK: https://www.tandfonline.com/doi/abs/10.1081/TT-200053935 Keywords: Three-phase
flow, Operator Splitting, Transitional waves, Central schemes for hyperbolic
conservation laws, Riemann problem, Secondary recovery.
[1] Eduardo Abreu, Fred Furtado, Dan Marchesin and Felipe
Pereira (2004), Transitional Waves in Three-Phase Flows in
Heterogeneous Formations In: Computational Methods for Water Resources, I.5
Unsaturated and Multi-phase, Developments in Water Science Volume 55, Part 1,
2004, Pages 609-620. LINK: https://doi.org/10.1016/S0167-5648(04)80085-6 Keywords: Three-phase
flow, Transitional waves, Heterogeneity, Conservation laws, Mixed finite
elements methods, Modeling and simulation of multi-scale phenomena.