22 citations · 27 across the 12 of their papers we have counts for
10 papers · 1 filter
Mathematical properties and numerical approximation of pseudo-parabolic systems
E. Abreu, E. Cuesta, A. Duran +1
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathem…
A geometrically intrinsic Lagrangian-Eulerian scheme for 2D Shallow Water Equations with variable topography and discontinuous data
Eduardo Abreu, Elena Bachini, John Perez +1
We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored…
Convergence of a Lagrangian-Eulerian scheme by a weak asymptotic analysis for one-dimensional hyperbolic problems
Eduardo Abreu, Arthur Espírito Santo, Wanderson Lambert +1
In this paper, we study both convergence and bounded variation properties of a new fully discrete conservative Lagrangian--Eulerian scheme to the entropy solution in the sense of K…
A study on a feedforward neural network to solve partial differential equations in hyperbolic-transport problems
Eduardo Abreu, Joao B. Florindo
In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we…
Recursive formulation and parallel implementation of multiscale mixed methods
E. Abreu, P. Ferraz, A. M. Espírito Santo +3
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art…
On the conservation properties in multiple scale coupling and simulation for Darcy flow with hyperbolic-transport in complex flows
Juan Galvis, Eduardo Abreu, Ciro Diaz +1
We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogene…
Error estimates for semidiscrete Galerkin and collocation approximations to pseudo-parabolic problems with Dirichlet conditions
Eduardo Abreu, Angel Durán
This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estima…
On the use of spectral discretizations with time strong stability preserving properties to Dirichlet pseudo-parabolic problems
Eduardo Abreu, Angel Durán
This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are dis…
A convergence analysis of Generalized Multiscale Finite Element Methods
Eduardo Abreu, Ciro Diaz, Juan Galvis
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We ob…
On high-order conservative finite element methods
Eduardo Abreu, Ciro Diaz, Juan Galvis +1
A new high-order conservative finite element method for Darcy flow is presented. The key ingredient in the formulation is a volumetric, residual-based, based on Lagrange multiplier…