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

Lakkis, Omar, Makridakis, Charalambos and Pryer, Tristan (2014) A comparison of duality and energy a posteriori estimates for L∞(0,T;L2(Ω)) in parabolic problems. Mathematics of Computation, 84 (294). pp. 1537-1569. ISSN 0025-5718

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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 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 -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
Keywords: Aposteriori error estimate, Convergence, Dissipation, Duality, Elliptic reconstruction, Finite element methods, Heat equation, Linear parabolic PDE, Optimality, Reaction-diffusion, Superconvergence
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Omar Lakkis
Date Deposited: 16 Feb 2016 08:56
Last Modified: 05 Aug 2019 14:30
URI: http://sro.sussex.ac.uk/id/eprint/59659

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