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A new two grid variational multiscale method for steady‐state natural convection problem
Author(s) -
Kong QiongXiang,
Yang YunBo
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3843
Subject(s) - gauss , grid , mathematics , computation , convergence (economics) , finite element method , stability (learning theory) , natural convection , operator (biology) , mathematical optimization , projection (relational algebra) , convection , computer science , algorithm , geometry , mechanics , physics , biochemistry , chemistry , quantum mechanics , repressor , machine learning , transcription factor , gene , economics , thermodynamics , economic growth
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.