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.
@article{M2AN_2011__45_5_915_0,
author = {K\v r\'\i \v zek, Michal and Roos, Hans-Goerg and Chen, Wei},
title = {Two-sided bounds of the discretization error for finite elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {915-924},
doi = {10.1051/m2an/2011003},
mrnumber = {2817550},
zbl = {1269.65113},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2011__45_5_915_0}
}
Křížek, Michal; Roos, Hans-Goerg; Chen, Wei. Two-sided bounds of the discretization error for finite elements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 915-924. doi : 10.1051/m2an/2011003. http://gdmltest.u-ga.fr/item/M2AN_2011__45_5_915_0/
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