Adaptivity and a Posteriori Error Control for Bifurcation Problems I: The Bratu Problem (Communications in Computational Physics, 2010)
This article is concerned with the numerical detection of bifurcation pointsof nonlinear partial differential equations as some parameter of interest is varied. Inparticular, we study in detail the numerical approximation of the Bratu problem, basedon exploiting the symmetric version of the interior penalty discontinuous Galerkinfinite element method. A framework for a posteriori control of the discretization errorin the computed critical parameter value is developed based upon the application ofthe dual weighted residual (DWR) approach. Numerical experiments are presented tohighlight the practical performance of the proposed a posteriori error estimator.