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Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

Cliffe, Andrew; Hall, Edward; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G.

Authors

Andrew Cliffe Andrew.Cliffe@nottingham.ac.uk

Edward Hall Edward.Hall@nottingham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk

Eric T. Phipps etphipp@sandia.gov

Andrew G. Salinger agsalin@sandia.gov



Abstract

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

Journal Article Type Article
Publication Date Oct 1, 2010
Journal Communications in Computational Physics
Electronic ISSN 1815-2406
Peer Reviewed Not Peer Reviewed
Volume 8
Issue 4
Pages 845-865
APA6 Citation Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. (2010). Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8(4), (845-865). doi:10.4208/cicp.290709.120210a. ISSN 1815-2406
DOI https://doi.org/10.4208/cicp.290709.120210a
Publisher URL http://www.global-sci.com/freedownload/v8_845.pdf
Related Public URLs http://www.global-sci.com
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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