计算数学 1998, 20(4) 431-448 DOI:     ISSN: 0254-7791 CN: 11-2125/O1

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热传导-对流问题;非线性Galerkin混合元法;全离散化格式
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PubMed

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅱ):向后一步的Euler全离散化格式

罗振东,王烈衡

中国科学院计算数学与科学工程计算所,中国科学与工程计算国家重点实验室

摘要

关键词 热传导-对流问题;非线性Galerkin混合元法;全离散化格式  

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR THE NON STATIONARY CONDUCTION-CONVECTION PROBLEMS (Ⅱ): THE BACKWARD ONE-STEP EULER FULLY DISCRETE FORMAT

Luo Zhen-Dong; Wang Lie-Heng (State Key Laboratory of Scientific/Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Chinese Academy of Sciences, Beijing)

Abstract:

In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity, defined respectively on a coarse grid with grids size H and another fine grid with grid size h<< H, a finite element space Mh for the approximation of the pressure and two finite element spaces AH and Wh, for the approximation of the temperature,also defined respectivply on the coarse grid with grid size H and another fine grid with grid size h. The existence and the convergence of the fully discrete mixed element solution are shown. The scheme consists in using standard backward one step Euler-Galerkin fully discrete format at first L0 steps (L0 2) on fine grid with grid size h, but using nonlinear Galerkin mixed element method of backward one step Euler-Galerkin fully discrete format through L0 + 1 step to end step. We have proved that the fully discrete nonlinear Galerkin mixed element procedure with respect to the coarse grid spaces with grid size H holds superconvergence.

Keywords: conduction-convection problems, nonlinear Galerkin mixed element method, fully discrete format.  
收稿日期  修回日期  网络版发布日期 1998-04-14 00:00:00.0 
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