Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems

Sergey Repin ()
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Sergey Repin: Russian Academy of Sciences, St. Petersburg Division of the Steklov Mathematical Institute

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 135-150 from Springer

Abstract: Abstract The paper is concerned with functional approach to the a posteriori error control for approximate solutions of differential equations. Functional a posteriori estimates are derived by purely functional methods using the analysis of variational problems or integral identities. They are intended to give computable minorants and majorants for various measures of the difference between exact solutions and their conforming approximations. Functional estimates contain no mesh dependent constants and provide guaranteed lower and upper bounds of errors. In this paper, the major attention is paid on a posteriori estimates in terms of local norms or locally based linear functionals. It is shown that for linear elliptic and parabolic problems functional estimates in global (energy) norms imply a posteriori estimates in terms of local quantities.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_8

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DOI: 10.1007/978-3-540-34288-5_8

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