- Title
- A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems
- Creator
- Lamichhane, Bishnu P.
- Relation
- Journal of Computational and Applied Mathematics Vol. 235, Issue 17, p. 5188-5197
- Publisher Link
- http://dx.doi.org/10.1016/j.cam.2011.05.005
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2011
- Description
- 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.
- Subject
- biharmonic equation; clamped plate; mixed finite element method; saddle point problem; biorthogonal system; a priori estimate
- Identifier
- http://hdl.handle.net/1959.13/937014
- Identifier
- uon:12470
- Identifier
- ISSN:0377-0427
- Language
- eng
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