On an Essential Estimate in the Analysis of Domain Decomposition Methods

Abstract

A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.