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Volume 8, Issue 4
Adaptivity and a Posteriori Error Control for Bifurcation Problems I: The Bratu Problem

K. Andrew Cliffe, Edward J. C. Hall, Paul Houston, Eric T. Phipps & Andrew G. Salinger

DOI: 10.4208/cicp.290709.120210a

Commun. Comput. Phys., 8 (2010), pp. 845-865.

Published online: 2010-08

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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.

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@Article{CiCP-8-845, author = {K. Andrew Cliffe, Edward J. C. Hall, Paul Houston, Eric T. Phipps and Andrew G. Salinger}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.290709.120210a}, url = {http://global-sci.org/intro/article_detail/cicp/7598.html} }
TY - JOUR T1 - Adaptivity and a Posteriori Error Control for Bifurcation Problems I: The Bratu Problem AU - K. Andrew Cliffe, Edward J. C. Hall, Paul Houston, Eric T. Phipps & Andrew G. Salinger JO - Communications in Computational Physics VL - 4 SP - 845 EP - 865 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.290709.120210a UR - https://global-sci.org/intro/article_detail/cicp/7598.html KW - AB -

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.

K. Andrew Cliffe, Edward J. C. Hall, Paul Houston, Eric T. Phipps and Andrew G. Salinger. (2010). Adaptivity and a Posteriori Error Control for Bifurcation Problems I: The Bratu Problem. Communications in Computational Physics. 8 (4). 845-865. doi:10.4208/cicp.290709.120210a
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