Norms of discrete trace functions of H 1(Ω) and H 2(Ω)

Jinchao Xu; Shuo Zhang

doi:10.2478/cmam-2012-0025

Norms of discrete trace functions of H 1(Ω) and H 2(Ω)

Jinchao Xu, Shuo Zhang

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of H 1(Ω) and H 2(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. © 2012 Institute of Mathematics, NAS of Belarus.

Original language	English (US)
Pages (from-to)	500-512
Number of pages	13
Journal	Computational Methods in Applied Mathematics
Volume	12
Issue number	4
DOIs	https://doi.org/10.2478/cmam-2012-0025
State	Published - Oct 1 2012
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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AB - This paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of H 1(Ω) and H 2(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. © 2012 Institute of Mathematics, NAS of Belarus.

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Norms of discrete trace functions of H 1(Ω) and H 2(Ω)

Abstract

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