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.

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.

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. https://doi.org/10.4208/cicp.290709.120210a

• Journal Article Type: Article
• Acceptance Date: Feb 12, 2010
• Online Publication Date: May 17, 2010
• Publication Date: Oct 1, 2010
• Deposit Date: Oct 5, 2012
• Publicly Available Date: Oct 5, 2012
• Journal: Communications in Computational Physics
• Electronic ISSN: 1815-2406
• Peer Reviewed: Not Peer Reviewed
• Volume: 8
• Issue: 4
• Pages: 845-865
• DOI: https://doi.org/10.4208/cicp.290709.120210a
• Public URL: https://nottingham-repository.worktribe.com/output/1011695
• Publisher URL: http://www.global-sci.com/freedownload/v8_845.pdf