Počet záznamů: 1
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
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SYSNO ASEP 0342835 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers Tvůrce(i) Jiránek, P. (CZ)
Strakoš, Zdeněk (UIVT-O) SAI, RID, ORCID
Vohralík, M. (FR)Zdroj.dok. SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275
Roč. 32, č. 3 (2010), s. 1567-1590Poč.str. 24 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova second-order elliptic partial differential equation ; finite volume method ; a posteriori error estimates ; iterative methods for linear algebraic systems ; conjugate gradient method ; stopping criteria Vědní obor RIV BA - Obecná matematika CEP IAA100300802 GA AV ČR - Akademie věd CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000278576300022 EID SCOPUS 77953840991 DOI 10.1137/08073706X Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2011
Počet záznamů: 1