Mixed finite element methods for the poisson equation using biorthogonal and quasi-biorthogonal systems

Title: Mixed finite element methods for the poisson equation using biorthogonal and quasi-biorthogonal systems
Creator: Lamichhane, Bishnu P.
Relation: Advances in Numerical Analysis Vol. 2013, no. 189045
Publisher Link: http://dx.doi.org/10.1155/2013/189045
Publisher: Hindawi
Resource Type: journal article
Date: 2013
Description: 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.
Subject: Poisson equation; finite element methods; Lagrange multiplier space; quasi-biorthogonal Systems
Identifier: http://hdl.handle.net/1959.13/1340260
Identifier: uon:28429
Identifier: ISSN:1687-9562
Rights: Copyright © 2013 Bishnu P. Lamichhane. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Language: eng
Full Text
Reviewed

		Thumbnail	File	Description	Size	Format
View Details Download			ATTACHMENT02	Publisher version (open access)	1 MB	Adobe Acrobat PDF	View Details Download