We propose and study a posteriori error estimates for convection–diffusion–reaction
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …

For the finite volume discretization of a second-order elliptic model problem, we derive a
posteriori error estimates which take into account an inexact solution of the associated linear …

Recently, engineers, scientists, and mathematicians have concentrated their efforts on
numerical methods for solving the Navier–Stokes equations. The reason is that these …

We derive a posteriori error estimates for the discretization of the heat equation in a unified
and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and …

In this paper, we develop a new mixed finite element method for elliptic problems on general
quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme …

Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is
developed. It is based on H^ 1_0 (Ω)^ d-conforming velocity reconstruction and H (div, Ω) …

This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …

We derive in this paper a unified framework for a priori and a posteriori error analysis of
mixed finite element discretizations of second-order elliptic problems. It is based on the …

In this work we propose and investigate the performance of a metric-based refinement
criteria for adaptive meshing used for improving the numerical solution of an elliptic problem …