Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems. (11th April 2013)

• Record Type: Journal Article
• Authors: Lamichhane, Bishnu P.
• Other Names: Heuer Norbert Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2013(2013)
• Publication Date: 2013-04-11
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2013/189045
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.