Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations

Şimşek, G. and Wu, X. and van der Zee, K.G. and van Brummelen, E.H. (2015) Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations. Computer Methods in Applied Mechanics and Engineering, 288 . pp. 83-109. ISSN 1879-2138

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Abstract

We introduce a duality-based two-level error estimator for linear and nonlinear time-dependent problems. The error measure can be a space-time norm, energy norm, final-time error or other error related functional. The general methodology is developed for an abstract nonlinear parabolic PDE and subsequently applied to linear heat and nonlinear Cahn-Hilliard equations. The error due to finite element approximations is estimated with a residual weighted approximate-dual solution which is computed with two primal approximations at nested levels. We prove that the exact error is estimated by our estimator up to higher-order remainder terms. Numerical experiments confirm the theory regarding consistency of the dual-based two-level estimator. We also present a novel space-time adaptive strategy to control errors based on the new estimator.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1016/j.cma.2014.11.019
Depositing User: van der Zee, Kristoffer
Date Deposited: 07 Apr 2016 07:52
Last Modified: 15 Sep 2016 15:38
URI: http://eprints.nottingham.ac.uk/id/eprint/32682

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