| Issue |
ESAIM: M2AN
Volume 45, Number 5, September-October 2011
|
|
|---|---|---|
| Page(s) | 915 - 924 | |
| DOI | https://doi.org/10.1051/m2an/2011003 | |
| Published online | 06 April 2011 | |
Two-sided bounds of the discretization error for finite elements
1
Institute of Mathematics, Academy of Sciences,
Žitná 25, 115 67 Prague 1, Czech Republic. krizek@math.cas.cz
2
Institute of Numerical Mathematics, Technical
University Dresden,
Zellescher Weg 12–14, 01069 Dresden, Germany. hans-goerg.roos@tu-dresden.de
3
School of Economics, Shandong University,
27 Shanda Nanlu, Jinan 250 100, P.R. China.
weichen@sdu.edu.cn
Received:
8
July
2010
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.
Mathematics Subject Classification: 65N30
Key words: Lagrange finite elements / Céa's lemma / superconvergence / lower error estimates.
© EDP Sciences, SMAI, 2011
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