Journal of Applied Mathematics
Volume 2013 (2013), Article ID 951692, 10 pages
http://dx.doi.org/10.1155/2013/951692
Research Article

A New Characteristic Nonconforming Mixed Finite Element Scheme for Convection-Dominated Diffusion Problem

Dongyang Shi,1 Qili Tang,1,2 and Yadong Zhang3

1Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
2School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
3School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China

Received 14 December 2012; Accepted 23 March 2013

Academic Editor: Junjie Wei

Copyright © 2013 Dongyang Shi 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

A characteristic nonconforming mixed finite element method (MFEM) is proposed for the convection-dominated diffusion problem based on a new mixed variational formulation. The optimal order error estimates for both the original variable and the auxiliary variable with respect to the space are obtained by employing some typical characters of the interpolation operator instead of the mixed (or expanded mixed) elliptic projection which is an indispensable tool in the traditional MFEM analysis. At last, we give some numerical results to confirm the theoretical analysis.