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Functional a posteriori error estimates for elliptic problems in exterior domains

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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.

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References

  1. R. Leis, Initial Boundary Value Problems in Mathematical Physics, Teubner, Stuttgart (1986).

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  2. S. Repin, “A posteriori error estimates for variational problems with uniformly convex functionals,” Math. Comp. 69, 481–500 (2000).

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  3. S. Repin, A Posteriori Estimates for Partial Differential Equations, Walter de Gruyter, Berlin (2008).

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  4. J. Saranen, K.-J. Witsch, “Exterior boundary value problems for elliptic equations,” Ann. Acad. Sci. Fenn. Math. 8, No. 1, 3–42 (1983).

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Authors and Affiliations

  1. University of Duisburg-Essen, Universitätsstr. 2, 45117, Essen, Germany

    Dirk Pauly

  2. University of Jyväskylä, P.O. Box 35 (Agora), FI-40014, Jyväskylä, Finland

    Dirk Pauly & Sergei Repin

  3. Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, 191011, Russia

    Sergei Repin

Authors
  1. Dirk Pauly
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  2. Sergei Repin
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Correspondence to Sergei Repin.

Additional information

Translated from Problemy Matematicheskogo Analiza, 42, August 2009, pp. 83–94.

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Pauly, D., Repin, S. Functional a posteriori error estimates for elliptic problems in exterior domains. J Math Sci 162, 393–406 (2009). https://doi.org/10.1007/s10958-009-9643-4

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  • DOI: https://doi.org/10.1007/s10958-009-9643-4

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