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Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations
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SYSNO ASEP 0428023 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations Author(s) Papež, Jan (UIVT-O) RID, SAI
Liesen, J. (DE)
Strakoš, Z. (CZ)Source Title Linear Algebra and Its Applications. - : Elsevier - ISSN 0024-3795
Roč. 449, 15 May (2014), s. 89-114Number of pages 26 s. Language eng - English Country US - United States Keywords numerical solution of partial differential equations ; finite element method ; adaptivity ; a posteriori error analysis ; discretization error ; algebraic error ; spatial distribution of the error Subject RIV BA - General Mathematics R&D Projects IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) GA201/09/0917 GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000336699600008 EID SCOPUS 84897676626 DOI 10.1016/j.laa.2014.02.009 Annotation In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary value model problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is not restricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2015
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