The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

We present equilibrated flux a posteriori error estimates in a unified setting for conforming,
nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two …

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

This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

Recently, the adaptive finite element methods have gained a very important position among
numerical procedures for solving ordinary as well as partial differential equations arising …

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 …

In this contribution we consider localized, robust, and efficient a posteriori error estimation of
the localized reduced basis multiscale (LRBMS) method for parametric elliptic problems with …

We derive a posteriori error estimates for a class of second-order monotone quasi-linear
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …