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

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
Reviewed

		Thumbnail	File	Description	Size	Format