Adaptivity and a Posteriori Error Control for Bifurcation Problems I: the Bratu Problem
| Autor: | K. Andrew Cliffe, Andrew G. Salinger, Edward Hall, Paul Houston, Eric T. Phipps |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Method of mean weighted residuals
Nonlinear system Mathematical optimization Partial differential equation Physics and Astronomy (miscellaneous) Discontinuous Galerkin method MathematicsofComputing_NUMERICALANALYSIS Applied mathematics Estimator A priori and a posteriori Bifurcation Finite element method Mathematics |
| Zdroj: | Communications in Computational Physics. 8:845-865 |
| ISSN: | 1991-7120 1815-2406 |
| DOI: | 10.4208/cicp.290709.120210a |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|