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Functional a posteriori error estimates for elliptic problems in exterior domains

  • Dirk Pauly
  • Sergei Repin
Article

This paper is concerned with the derivation of computable and guaranteed upper bounds of the difference between the exact and approximate solutions of an exterior domain boundary value problem for a linear elliptic equation. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the estimates derived in the paper at hand are applicable to any approximate solution that belongs to the corresponding energy space. Such estimates (also called error majorants of functional type) were derived earlier for problems in bounded domains of RN. Bibliography: 4 titles. Illustrations: 1 figure.

Keywords

Triangle Inequality Schwarz Inequality Extension Operator Exterior Domain Posteriori Error Estimate 
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References

  1. 1.
    R. Leis, Initial Boundary Value Problems in Mathematical Physics, Teubner, Stuttgart (1986).MATHGoogle Scholar
  2. 2.
    S. Repin, “A posteriori error estimates for variational problems with uniformly convex functionals,” Math. Comp. 69, 481–500 (2000).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Repin, A Posteriori Estimates for Partial Differential Equations, Walter de Gruyter, Berlin (2008).MATHCrossRefGoogle Scholar
  4. 4.
    J. Saranen, K.-J. Witsch, “Exterior boundary value problems for elliptic equations,” Ann. Acad. Sci. Fenn. Math. 8, No. 1, 3–42 (1983).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.University of Duisburg-EssenEssenGermany
  2. 2.University of JyväskyläJyväskyläFinland
  3. 3.Steklov Mathematical Institute RASSt. PetersburgRussia

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