A variational multiscale method for steady natural convection problem based on two-grid discretization

Advances in Difference Equations

Tong Zhang¹  Xuesi Ma²  ZhenZhen Tao³ 

[1] Information Science, Henan Polytechnic University, Jiaozuo, P.R. China;Center for Intelligence Science and Technology, School of Computer Science, Beijing University of Posts and Telecommunications, Beijing, P.R. China;School of Mathematics &

关键词: natural convection problem;    two-grid discretization;    Oseen iteration;    variational multiscale method;    error estimates;   

DOI  :  10.1186/s13662-016-0815-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose and analyze a two-grid variational multiscale method for the steady natural convection problem based on two local Gauss integrations technique. This method possesses the best algorithmic characteristics of both variational multiscale method and two-grid discretization. The main idea is to first solve the nonlinear steady natural convection problem on the coarse grid, then to use the coarse grid solution to fix the nonlinear terms, and to solve a linear problem on the fine grid. Stability and optimal error estimates of the discrete solutions in both one-grid and two-grid variational multiscale formulations are established. Finally, some numerical examples are presented to verify the method’s promise and testify the theoretical predictions.

【 授权许可】

CC BY