Chapter 6 A posteriori error estimates for finite element approximations 6 . 1 Introduction

The a posteriori error estimation of finite element approximations of elliptic boundary value problems has reached some state of maturity, as it is documented by a variety of monographs on this subject (cf., e.g., [1, 2, 3, 4, 5]). There are different concepts such as • residual type a posteriori error estimators, • hierarchical type a posteriori error estimators, • error estimators based on local averaging, • error estimators based on the goal oriented weighted dual approach (cf., in particular, [3]). In this chapter, we will focus on residual type a posteriori error estimators and follow the exposition in [5].