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A Posteriori Error Estimation in Terms of Linear Functionals for Boundary Value Problems of Elliptic Type

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Sergey Korotov

    (University of Jyväskylä, Department of Mathematical Information Technology)

  • Pekka Neittaanmäki

    (University of Jyväskylä, Department of Mathematical Information Technology)

  • Sergey Repin

    (V.A. Steklov Institute of Mathematics in St.-Petersburg)

Abstract

Summary The paper deals with a posteriori error estimation in terms of special problem-oriented quantities, represented as a linear functionals that control the behavior of a solution in certain subdomains, along some lines, or at especially interesting points. The method of estimating such quantities is based on the analysis of the adjoint boundary-value problems, whose right-hand sides are formed by the considered linear functionals. On this way, we propose a new effective approach based on two principles: (a) the original and adjoint problems are solved on non-coinciding meshes, and (b) the term presenting the product of gradients of errors of the primal and adjoint problems is estimated by using the “gradient averaging” technique. The model problem of elliptic type is analysed and the results of numerical tests are presented.

Suggested Citation

  • Sergey Korotov & Pekka Neittaanmäki & Sergey Repin, 2004. "A Posteriori Error Estimation in Terms of Linear Functionals for Boundary Value Problems of Elliptic Type," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 587-595, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_56
    DOI: 10.1007/978-3-642-18775-9_56
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