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)
Official URL: http://www.global-sci.com/freedownload/v8_845.pdf
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.
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