Convergence of simple adaptive Galerkin schemes based on h - h/2 error estimators

Abstract

We discuss several adaptive mesh-refinement strategies based on (h - h/2)-error estimation. This class of adaptive methods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general. © The Author(s) 2010.