Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 747391, 14 pages
Research Article

A Finite Element Variational Multiscale Method Based on Two Local Gauss Integrations for Stationary Conduction-Convection Problems

1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
2Center for Computational Geosciences, Xi'an Jiaotong University, Xi'an 710049, China
3China Nuclear Power Simulation Technology Company Limited, Shenzhen 518115, China
4College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, China

Received 6 July 2012; Revised 23 October 2012; Accepted 24 October 2012

Academic Editor: Hung Nguyen-Xuan

Copyright © 2012 Yu Jiang 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.


A new finite element variational multiscale (VMS) method based on two local Gauss integrations is proposed and analyzed for the stationary conduction-convection problems. The valuable feature of our method is that the action of stabilization operators can be performed locally at the element level with minimal additional cost. The theory analysis shows that our method is stable and has a good precision. Finally, the numerical test agrees completely with the theoretical expectations and the “ exact solution,” which show that our method is highly efficient for the stationary conduction-convection problems.