A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems

作者：Lamichhane Bishnu P^*

来源：Journal of Computational and Applied Mathematics, 2011, 235(17): 5188-5197.

DOI：10.1016/j.cam.2011.05.005

• Biharmonic equation
• Clamped plate
• Mixed finite element method
• Saddle point problem
• Biorthogonal system
• A priori estimate

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.

• 出版日期2011-7-1