Norms of Discrete Trace Functions of (Ω) and (Ω)
Jinchao Xu, Shuo Zhang · Computational Methods in Applied Mathematics · 2012
Abstract This paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of H¹ (Ω) and H² (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.