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

共 50 条

[21] A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem [J].

Ainsworth, M ;

Kelly, DW .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2001, 15 (1-4) :3-23

[22] A POSTERIORI ERROR ESTIMATES FOR THE ALLEN-CAHN PROBLEM [J].

Chrysafinos, Konstantinos ;

Georgoulis, Emmanuil H. ;

Plaka, Dimitra .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (05) :2662-2683

[23] Inhomogeneous Dirichlet boundary condition in the a posteriori error control of the obstacle problem [J].

Gaddam, Sharat ;

Gudi, Thirupathi .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (07) :2311-2327

[24] A POSTERIORI ERROR ESTIMATION FOR hp-ADAPTIVITY FOR FOURTH-ORDER EQUATIONS [J].

Moore, Peter K. ;

Rangelova, Marina .

MATHEMATICS OF COMPUTATION, 2010, 79 (270) :677-705

[25] A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems [J].

Adjerid, S ;

Devine, KD ;

Flaherty, JE ;

Krivodonova, L .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (11-12) :1097-1112

[26] An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems [J].

Georgoulis, Emmanuil H. ;

Houston, Paul ;

Virtanen, Juha .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (01) :281-298

[27] A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models [J].

Tirvaudey, Marie ;

Chamoin, Ludovic ;

Bouclier, Robin ;

Passieux, Jean-Charles .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, 367

[28] A posteriori error estimation and adaptivity based on VMS for the incompressible Navier-Stokes equations [J].

Irisarri, Diego ;

Hauke, Guillermo .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2021, 373

[29] A posteriori error estimates and adaptivity for the continuous Galerkin time-stepping method for nonlinear initial value problems [J].

Tian, Liutao ;

Yang, Shuo ;

Tian, Hongjiong .

CALCOLO, 2025, 62 (02)

[30] A posteriori error estimation and adaptivity in the method of lines with mixed finite elements [J].

Brandts J.H. .

Applications of Mathematics, 1999, 44 (6) :407-419

← 1 2 3 4 5 →