Two-sided bounds of the discretization error for finite elements

Michal Křížek; Hans-Goerg Roos; Wei Chen

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 5, page 915-924
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Křížek, Michal, Roos, Hans-Goerg, and Chen, Wei. "Two-sided bounds of the discretization error for finite elements." ESAIM: Mathematical Modelling and Numerical Analysis 45.5 (2011): 915-924. <http://eudml.org/doc/197508>.

@article{Křížek2011,
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. },
author = {Křížek, Michal, Roos, Hans-Goerg, Chen, Wei},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Lagrange finite elements; Céa's lemma; superconvergence; lower error estimates.; Céa’s lemma; superconvergence; lower error estimates; numerical examples; elliptic problem},
language = {eng},
month = {4},
number = {5},
pages = {915-924},
publisher = {EDP Sciences},
title = {Two-sided bounds of the discretization error for finite elements},
url = {http://eudml.org/doc/197508},
volume = {45},
year = {2011},
}

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
DA - 2011/4//
PB - EDP Sciences
VL - 45
IS - 5
SP - 915
EP - 924
AB - 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.
LA - eng
KW - Lagrange finite elements; Céa's lemma; superconvergence; lower error estimates.; Céa’s lemma; superconvergence; lower error estimates; numerical examples; elliptic problem
UR - http://eudml.org/doc/197508
ER -

References

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