Non Shape Regular Domain Decompositions: An Analysis Using a Stable Decomposition in H01

Abstract

In this paper, we establish the existence of a stable decomposition in the Sobolev space H01 for domain decompositions which are not shape regular in the usual sense. In particular, we consider domain decompositions where the largest subdomain is significantly larger than the smallest subdomain. We provide an explicit upper bound for the stable decomposition that is independent of the ratio between the diameter of the largest and the smallest subdomain. © Springer-Verlag Berlin Heidelberg 2013.