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Complementarity based a posteriori error estimates and their properties
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SYSNO ASEP 0379721 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Complementarity based a posteriori error estimates and their properties Author(s) Vejchodský, Tomáš (MU-W) RID, SAI, ORCID Source Title Mathematics and Computers in Simulation. - : Elsevier - ISSN 0378-4754
Roč. 82, č. 10 (2012), s. 2033-2046Number of pages 14 s. Language eng - English Country NL - Netherlands Keywords error majorant ; a posteriori error estimates ; method of hypercircle Subject RIV BA - General Mathematics R&D Projects GA102/07/0496 GA ČR - Czech Science Foundation (CSF) IAA100760702 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000308519900023 EID SCOPUS 84865804139 DOI https://doi.org/10.1016/j.matcom.2011.06.001 Annotation The paper is devoted to complementary approaches in a posteriori error estimation for a diffusion-reaction model problem. These approaches provide sharp and guaranteed upper bounds for the energy norm of the error and they are independent from the way how the approximate solution is obtained. In particular, the estimator naturally includes all sources of errors of any conforming approximation, like the discretization error, the error in the solver of linear algebraic systems, the quadrature error, etc. The paper recapitulates three complementarity approaches, proves sufficient and necessary conditions for the efficiency and asymptotic exactness of the error estimators, constructs an approximation by the method of hypercircle such that its error can be computed exactly, and presents numerical tests showing robustness of these approaches. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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