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A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
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SYSNO ASEP 0342835 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers Author(s) Jiránek, P. (CZ)
Strakoš, Zdeněk (UIVT-O) SAI, RID, ORCID
Vohralík, M. (FR)Source Title SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275
Roč. 32, č. 3 (2010), s. 1567-1590Number of pages 24 s. Language eng - English Country US - United States Keywords second-order elliptic partial differential equation ; finite volume method ; a posteriori error estimates ; iterative methods for linear algebraic systems ; conjugate gradient method ; stopping criteria Subject RIV BA - General Mathematics R&D Projects IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000278576300022 EID SCOPUS 77953840991 DOI 10.1137/08073706X Annotation For the finite volume discretization of a second-order elliptic model problem, we derive a posteriori error estimates which take into account an inexact solution of the associated linear algebraic system. We show that the algebraic error can be bounded by constructing an equilibrated Raviart-Thomas-Nédélec discrete vector field whose divergence is given by a proper weighting of the residual vector. Next, claiming that the discretization error and the algebraic one should be in balance, we construct stopping criteria for iterative algebraic solvers.Using this convenient balance, we also prove the efficiency of our a posteriori estimates; i.e., we show that they also represent a lower bound, up to a generic constant, for the overall energy error. A local version of this result is also stated. This makes our approach suitable for adaptive mesh refinement which also takes into account the algebraic error. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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