Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method

W Dahmen, B Faermann, I G Graham, W Hackbusch, S A Sauter

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly non-quasi-uniform) meshes. These inequalities involve norms of the form \\h(alpha)u\\(Ws,p) ((Omega)) for positive and negative s and alpha, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N, the total number of degrees of freedom in the finite element space, and we avoid estimates involving either the global maximum or minimum mesh diameter. Our inequalities include new variants of inverse inequalities as well as trace and extension theorems. They can be used in several areas of finite element analysis to extend results-previously known only for quasi-uniform meshes-to the locally re fined case. Here we describe applications to (i) the theory of nonlinear approximation and (ii) the stability of the mortar element method for locally refined meshes.
Original languageEnglish
Pages (from-to)1107-1138
Number of pages32
JournalMathematics of Computation (MCOM)
Volume73
Issue number247
Publication statusPublished - 2004

Fingerprint Dive into the research topics of 'Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method'. Together they form a unique fingerprint.

  • Cite this