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Two-sided bounds of the discretization error for finite elements

Published online by Cambridge University Press:  06 April 2011

Michal Křížek ,
Hans-Goerg Roos  and
Wei Chen
Michal Křížek
Affiliation:
Institute of Mathematics, Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic. krizek@math.cas.cz
Hans-Goerg Roos
Affiliation:
Institute of Numerical Mathematics, Technical University Dresden, Zellescher Weg 12–14, 01069 Dresden, Germany. hans-goerg.roos@tu-dresden.de
Wei Chen
Affiliation:
School of Economics, Shandong University, 27 Shanda Nanlu, Jinan 250 100, P.R. China. weichen@sdu.edu.cn
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Abstract

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.

Keywords

Lagrange finite elementsCéa's lemmasuperconvergencelower error estimates.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 5 , September 2011 , pp. 915 - 924
Copyright
© EDP Sciences, SMAI, 2011

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