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A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems
- Source :
-
Journal of Computational & Applied Mathematics . Jul2011, Vol. 235 Issue 17, p5188-5197. 10p. - Publication Year :
- 2011
-
Abstract
- Abstract: We propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition. The mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a Lagrange multiplier as new unknowns. Working with a pair of bases forming a biorthogonal system, we can easily eliminate the gradient of the solution and the Lagrange multiplier from the saddle point system leading to a positive definite formulation. Using a superconvergence property of a gradient recovery operator, we prove an optimal a priori estimate for the finite element discretization for a class of meshes. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 235
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 62270998
- Full Text :
- https://doi.org/10.1016/j.cam.2011.05.005