On Function Spaces Related to Finite Element Approximation Theory

Abstract

Certain function spaces of Besov type based on triangular finite elements in a two-dimensional domain are introduced and investigated. These spaces allow a systematic approach to the main estimates of finite element approximation theory in Besov-Sobolev norms, to the problem of improving the rate of approximation by choosing appropriate triangulations, and to asymptotic error estimates for elliptic boundary value problems.