@Article{CiCP-8-845,
author = {},
title = {Adaptivity and a Posteriori Error Control for Bifurcation Problems I: The Bratu Problem},
journal = {Communications in Computational Physics},
year = {2010},
volume = {8},
number = {4},
pages = {845--865},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290709.120210a},
url = {http://global-sci.org/intro/article_detail/cicp/7598.html}
}