# 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

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topKřížek, 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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