A comparison of duality and energy aposteriori estimates for L∞(0,T; L2(Ω)) in parabolic problems

Lakkis, Omar, Makridakis, Charalambos and Pryer, Tristan (2014) A comparison of duality and energy aposteriori estimates for L∞(0,T; L2(Ω)) in parabolic problems. Mathematics of Computation (MCOM), 2015 (84). pp. 1537-1569. ISSN 1088-6842

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We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the L∞(0,T; L2(Ω)) norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the L∞(0,T; L2(Ω))-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Samuel Appleton
Date Deposited: 29 Jul 2015 10:08
Last Modified: 14 Mar 2017 05:53
URI: http://sro.sussex.ac.uk/id/eprint/55813

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