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

Cliffe, Andrew and Hall, Edward and Houston, Paul and Phipps, Eric T. and Salinger, Andrew G. (2010) Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8 (4). pp. 845-865. ISSN 1815-2406 (Submitted)

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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.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
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Depositing User: Houston, Paul
Date Deposited: 05 Oct 2012 08:32
Last Modified: 05 Oct 2012 08:32
URI: http://eprints.nottingham.ac.uk/id/eprint/1099

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