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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 934973, 9 pages
http://dx.doi.org/10.1155/2013/934973
Research Article

Expanded Mixed Finite Element Method for the Two-Dimensional Sobolev Equation

1School of Mathematics, Shandong University, Jinan 250100, China
2School of Science, Shandong Jianzhu University, Jinan 250101, China

Received 23 April 2013; Revised 7 June 2013; Accepted 7 June 2013

Academic Editor: Carlos Conca

Copyright © 2013 Qing-li Zhao et al. 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.

Abstract

Expanded mixed finite element method is introduced to approximate the two-dimensional Sobolev equation. This formulation expands the standard mixed formulation in the sense that three unknown variables are explicitly treated. Existence and uniqueness of the numerical solution are demonstrated. Optimal order error estimates for both the scalar and two vector functions are established.