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Two-sided bounds of the discretization error for finite elements
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SYSNO ASEP 0359285 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Two-sided bounds of the discretization error for finite elements Author(s) Křížek, Michal (MU-W) RID, SAI, ORCID
Roos, H.-G. (DE)
Chen, W. (CN)Source Title E S A I M: Mathematical Modelling and Numerical Analysis - ISSN 0764-583X
Roč. 45, č. 5 (2011), s. 915-924Number of pages 10 s. Language eng - English Country FR - France Keywords Lagrange finite elements ; Céa's lemma ; superconvergence ; lower error estimates Subject RIV BA - General Mathematics R&D Projects IAA100190803 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000289628000006 EID SCOPUS 80051999217 DOI 10.1051/m2an/2011003 Annotation We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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