The following works have been published and made available online during December 2022 to February 2023:

An exponential integration generalized multiscale finite element method for parabolic problems.

Luis Hernandez, David Pardo, Eduardo Abreu, Judit Muñoz-Matute Ciro Díaz, Juan Galvis.

LINK: https://doi.org/10.1016/j.jcp.2023.112014

Keywords: Multiscale approximation, Time integration, Functions of matrices, Finite element methods.

Avaialble online on 21 February 2023

 

Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian-Eulerian scheme via weak asymptotic analysis for hyperbolic problems.  

Eduardo Abreu, Arthur Espírito Santo, Wanderson Lambert, Jonh Pérez. 

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.

Avaialble online on 26 December 2022. 

A geometrically intrinsic lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data. 

Eduardo Abreu, Elena Bachini, John Pérez, Mario Putti.

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.

Avaialble online on 21 December 2022