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.
Mots clés : Lagrange finite elements, Céa's lemma, superconvergence, lower error estimates
@article{M2AN_2011__45_5_915_0, author = {K\v{r}{\'\i}\v{z}ek, 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 }, pages = {915--924}, publisher = {EDP-Sciences}, volume = {45}, number = {5}, year = {2011}, doi = {10.1051/m2an/2011003}, mrnumber = {2817550}, zbl = {1269.65113}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2011003/} }
TY - JOUR AU - Křížek, Michal AU - Roos, Hans-Goerg AU - Chen, Wei TI - Two-sided bounds of the discretization error for finite elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 915 EP - 924 VL - 45 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011003/ DO - 10.1051/m2an/2011003 LA - en ID - M2AN_2011__45_5_915_0 ER -
%0 Journal Article %A Křížek, Michal %A Roos, Hans-Goerg %A Chen, Wei %T Two-sided bounds of the discretization error for finite elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 915-924 %V 45 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011003/ %R 10.1051/m2an/2011003 %G en %F 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 , Tome 45 (2011) no. 5, pp. 915-924. doi : 10.1051/m2an/2011003. http://www.numdam.org/articles/10.1051/m2an/2011003/
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