In this paper we review the basic concepts to obtain a posteriori error estimates for the finite
element solution of an elliptic linear model problem. We give the basic ideas to establish …

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

Self-adaptive discretization methods are now an indispensable tool for the numerical
solution of partial differential equations that arise from physical and technical applications …

The solution of elliptic boundary value problems may have anisotropic behaviour in parts of
the domain. That means that the solution varies signicantly only in certain directions …

Bibliography Page 1 Bibliography [1] Y. Achdou, C. Bernardi, and F. Coquel, A priori and a
posteriori analysis of finite volume dis- cretizations of Darcy’s equations, Numer. Math. 96 (2003) …

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 …

This is a survey on the theory of adaptive finite element methods (AFEM), which are
fundamental in modern computational science and engineering. We present a self …

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 …

The dual weighted residual method (DWR) and its localization for mesh adaptivity applied to
elliptic partial differential equations are investigated. The contribution of this paper is twofold …

A new computable a posteriori error estimator is introduced, which relies on the solution of
small discrete problems on stars. It exhibits built-in flux equilibration and is equivalent to the …