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

被引：9

作者：

Cliffe, K. Andrew ^{[1
]}

Hall, Edward J. C. ^{[1
]}

Houston, Paul ^{[1
]}

Phipps, Eric T. ^{[2
]}

Salinger, Andrew G. ^{[2
]}

机构：

[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[2] Sandia Natl Labs, Comp Sci Res Inst, Albuquerque, NM 87185 USA

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2010年 / 8卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Bifurcation theory; Bratu problem; a posteriori error estimation; adaptivity; discontinuous Galerkin methods; ELLIPTIC EIGENVALUE PROBLEMS; DISCONTINUOUS GALERKIN METHODS; FINITE-ELEMENT APPROXIMATIONS; NUMERICAL COMPUTATION; NONLINEAR PROBLEMS; BRANCH-POINTS; EQUATIONS;

D O I：

10.4208/cicp.290709.120210a

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：845 / 865

页数：21

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