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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

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Volume 12, Issue 4


Norms of Discrete Trace Functions of H¹(Ω) and H²(Ω)

Jinchao Xu
  • Center for Computational Mathematics and Applications, Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.
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Shuo Zhang
  • LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
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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

About the article

Received: 2012-03-22

Revised: 2012-07-30

Accepted: 2012-08-09

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 12, Issue 4, Pages 500–512, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2012-0025.

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