A new two grid variational multiscale method for steady‐state natural convection problem. (1st February 2016)

• Record Type: Journal Article
• Authors: Kong, Qiong‐Xiang; Yang, Yun‐Bo
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 14(2016:Sep. 30)
• Page Start: 4007
• Page End: 4024
• Publication Date: 2016-02-01
• Subjects: natural convection problem -- two‐grid method -- variational multiscale -- finite element method -- two local Gauss integrations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3843
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A two‐grid variational multiscale method based on two local Gauss integrations for solving the stationary natural convection problem is presented in this article. A significant feature of the method is that we solve the natural convection problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations firstly, and then find a fine grid solution by solving a linearized problem on a fine grid. In the computation, we introduce two local Gauss integrations as a stabilizing term to replace the projection operator without adding other variables. The stability estimates and convergence analysis of the new method are derived. Ample numerical experiments are performed to validate the theoretical predictions and demonstrate the efficiency of the new method. Copyright © 2016 John Wiley & Sons, Ltd.