Accessible Requires Authentication Published by De Gruyter January 1, 2012

Norms of Discrete Trace Functions of (Ω) and (Ω)

Jinchao Xu and Shuo Zhang

Abstract

This paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of (Ω) and (Ω) defined on the boundary or interface of an unstructured grid. We transform the nonlocal norms of trace functions to local norms of certain functions defined on the whole domain by constructing isomorphic extension operators. A unified approach is used to explore several typical examples. Additionally, we also discuss exactly invertible Poincaré–Steklov operators and their discretization.

Received: 2012-03-22
Revised: 2012-07-30
Accepted: 2012-08-9
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus