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

Şimşek, G.; Wu, X.; van der Zee, K.G.; van Brummelen, E.H.

Authors

G. Şimşek g.simsek@tue.nl

X. Wu x.wu@tue.nl

E.H. van Brummelen e.h.v.brummelen@tue.nl



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.

Journal Article Type Article
Publication Date May 1, 2015
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 288
APA6 Citation Şimşek, G., Wu, X., van der Zee, K., & van Brummelen, E. (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, doi:10.1016/j.cma.2014.11.019
DOI https://doi.org/10.1016/j.cma.2014.11.019
Publisher URL http://www.sciencedirect.com/science/article/pii/S0045782514004459
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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