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Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems

Authors: Omar Lakkis and Charalambos Makridakis
Journal: Math. Comp. 75 (2006), 1627-1658
MSC (2000): Primary 65N30
Published electronically: May 26, 2006
MathSciNet review: 2240628
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Abstract: We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of $ \operatorname{L}_\infty(0,T;\operatorname{L}_2(\Omega))$ and the higher order spaces, $ \operatorname{L}_\infty(0,T;\operatorname{H}^1(\Omega))$ and $ \operatorname{H}^1(0,T;\operatorname{L}_2(\Omega))$, with optimal orders of convergence.

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Additional Information

Omar Lakkis
Affiliation: Department of Mathematics, University of Sussex, Brighton, UK-BN1 9RF, United Kingdom

Charalambos Makridakis
Affiliation: Department of Applied Mathematics, University of Crete, GR-71409 Heraklion, Greece; and Institute for Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Vasilika Vouton P.O. Box 1527, GR-71110 Heraklion, Greece

Received by editor(s): December 26, 2003
Received by editor(s) in revised form: May 23, 2005
Published electronically: May 26, 2006
Additional Notes: The first author was supported by the E.U. RTN Hyke HPRN-CT-2002-00282 and the EU’s MCWave Marie Curie Fellowship HPMD-CT-2001-00121 during the preparation of this work at FORTH in Heraklion of Crete, Greece.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.