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

✍ Scribed by Bishnu P. Lamichhane

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 266 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2011.05.005

✦ Synopsis

A priori estimate a b s t r a c t

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.