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

Sergey Korotov (), Pekka Neittaanmäki () and Sergey Repin ()
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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

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 587-595 from Springer

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.

Keywords: Posteriori Error; Linear Functional; Posteriori Error Estimation; Galerkin Approximation; Adjoint Problem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_56

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DOI: 10.1007/978-3-642-18775-9_56

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