A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems |
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Authors: | Bishnu P. Lamichhane |
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Affiliation: | School of Mathematical & Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia Mathematical Sciences Institute, Australian National University, ACT 0200, Canberra, Australia |
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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. |
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Keywords: | 65N30 65N15 |
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