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The Scientific World Journal
Volume 2014, Article ID 297825, 13 pages
http://dx.doi.org/10.1155/2014/297825
Research Article

A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation

1School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China
2School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received 30 August 2013; Accepted 2 December 2013; Published 18 February 2014

Academic Editors: G. Fernandez-Anaya and L. Guerrini

Copyright © 2014 Jinfeng Wang 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

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in -norm for the scalar unknown and a priori error estimates in -norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in -norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method.