Adaptivity and A Posteriori Error Control for Bifurcation Problems Ⅰ:The Bratu Problem

查看全文 作　　者：K.Andrew [1]Cliffe;Edward [1]J.C.Hall;Paul [1]Houston;Eric [2]T.Phipps;Andrew [2]G.Salinger

机构地区：[1]School of Mathematical Sciences,University of Nottingham,University Park,Nottingham NG72RD,UK;[2]Computer Science Research Institute,Sandia National Laboratories,Albuquerque,New Mexico,USA

出　　处：《Communications in Computational Physics》索引2010年第8卷第9期,共21页

基　　金：the financial support of the EPSRC under the grant EP/E013724;the support of the EPSRC under the grant EP/F01340X. 摘　　要：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. 关键词：Bifurcation theory Bratu problem a posteriori error estimation adaptivity discontinuous Galerkin methods

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Adaptivity and A Posteriori Error Control for Bifurcation Problems Ⅰ:The Bratu Problem

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