A new two grid variational multiscale method for steady-state natural convection problem

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 mul...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2016-09, Vol.39 (14), p.4007-4024
Main Authors: Kong, Qiong-Xiang, Yang, Yun-Bo
Format: Article
Language:English
Subjects:
Convection
Convergence
Estimates
finite element method
Mathematical analysis
Mathematical models
Multiscale methods
natural convection problem
Operators
Stability
two local Gauss integrations
two-grid method
variational multiscale
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3843