On a general decomposition of the error of an approximate stress field in elasticity
Abstract
The errors of finite element approximations are analysed in a general frame, which is completely independent from the way through which the approximate solution was obtained. It is found that the error always admits decomposition in two terms, namely the equilibrium error and the compatibility error, which are orthogonal. Each of these admits upper and lower bounds that can be computed in a post-processing scheme.
References
[1] P. Beckers. Les Fonctions de Tension dans la Méthode des Eléments finis. Doctoral thesis, Univ. of Liège, Belgium, 1972.
[2] J.F. Debongnie. Sur une mesure locale de l'erreur de discrétisation par éléments finis. Univ. of Liège, Report LMF / D28, 1993.
[3] J.F. Debongnie. Une théorie abstraite des erreurs d'approximation des modèles d'éléments finis. Univ. of Liège, Report LMF / D32, 1994.
[4] J.F. Debongnie, H.G. Zhong, P. Beckers. Dual Analysis with general boundary conditions. Comput. Methods Appl. Engrg., 122: 183-192, 1995.
[5] P. Diez, J.J. Egozcue, A. Huerta. A posteriori error estimation for standard finite element analysis. Comput. Methods Appl. Mech. Engrg., 163: 141-157, 1998.
[2] J.F. Debongnie. Sur une mesure locale de l'erreur de discrétisation par éléments finis. Univ. of Liège, Report LMF / D28, 1993.
[3] J.F. Debongnie. Une théorie abstraite des erreurs d'approximation des modèles d'éléments finis. Univ. of Liège, Report LMF / D32, 1994.
[4] J.F. Debongnie, H.G. Zhong, P. Beckers. Dual Analysis with general boundary conditions. Comput. Methods Appl. Engrg., 122: 183-192, 1995.
[5] P. Diez, J.J. Egozcue, A. Huerta. A posteriori error estimation for standard finite element analysis. Comput. Methods Appl. Mech. Engrg., 163: 141-157, 1998.
Published
2023-03-02
Issue
pp. 261-270
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Debongnie, J.-F., & Beckers, P. (2023). On a general decomposition of the error of an approximate stress field in elasticity. Computer Assisted Methods in Engineering and Science, 8(2-3), 261-270. https://cames3.ippt.pan.pl/index.php/cames/article/view/1169
