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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 618258, 10 pages
http://dx.doi.org/10.1155/2015/618258
Research Article

The Time Discontinuous -Galerkin Mixed Finite Element Method for Linear Sobolev Equations

1Basic Subject Department, Shandong Women’s University, Jinan, Shandong 250300, China
2School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received 14 December 2014; Revised 18 March 2015; Accepted 19 March 2015

Academic Editor: Alicia Cordero

Copyright © 2015 Hong Yu 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 combine the -Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at most with the time variable. The existence and uniqueness of the solutions are proved, and the optimal -norm error estimates are derived. We get high accuracy for both the space and time variables.