Publications

Recent Publications (From 2020 to 2024)

For a complete list with selected publications, please see below.

[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/worldscinet/jhde). 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.

 

See below the complete list with selected publications 

(From 2004 to 2023)

 

[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.

[46] 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. 

[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.