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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.
Keywords: non-local norm; unstructured grid; isomorphic extension; conforming and nonconforming discretization; Poincaré–Steklov operator
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
