Journal of Applied Mathematics
Volume 2012 (2012), Article ID 391372, 24 pages
http://dx.doi.org/10.1155/2012/391372
Research Article

A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

Yang Liu,1 Hong Li,1 Jinfeng Wang,2 and Wei Gao1

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

Received 4 February 2012; Revised 3 April 2012; Accepted 19 April 2012

Academic Editor: Jinyun Yuan

Copyright © 2012 Yang Liu 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 new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.