On the Saturation Assumption and Hierarchical a Posteriori Error Estimator

Abstract

AbstractThe saturation assumption is widely used in a posteriori error analysis of finite element methods. It asserts, in its simplest form, that the solution can be approximated asymptotically with quadratic finite elements than with linear ones. In this paper, we show that a simple modification of this “hypothesis” is valid, and the proof of a posteriori error estimators by several authors becomes rigoruous with this simple modification.