四边形剖分下的组合多尺度有限元方法求解多尺度椭圆问题

• 作者: 和晓晓 宋飞 张振
• 来源期刊: 高等学校计算数学学报
• 学科: 数学
• 年，卷（期）: 2018,（4）
• 页码范围: 364-384
• 页数: 21页
• 分类号: O241
• 语种: 中文

摘要

The combined finite element and multiscale finite element method (FEMsFEM) [W.Deng and H.Wu,Multiscale Model.Simul.,12(2014),pp.1424-1457.]has been introduced for the multiscale elliptic problems.This is accomplished by using the standard finite element method on a fine mesh of the problematic part of the domain and using the oversampling MsFEM on a coarse mesh of the other part.The transmission condition across the FE-MsFE interface is treated by the penalty technique.FE-MsFEM can solve the multiscale elliptic problems with fine and long-ranged high contrast channels very efficiently.However,the detailed convergence analysis reveals that the error generated by the mismatch between the triangulation and the period of the coefficient still exists.A direct approach to reduce this error is to utilize the rectangle mesh for the domain.In this paper,we investigate the FE-MsFEM based on the rectangle mesh for the multiscale elliptic problems.Error estimate is given under the assumption that the oscillating coefficient is periodic.Numerical experiments for the rectangle mesh are carried out on the multiscale problems with periodic highly oscillating coefficient and high contrast channels.Their results demonstrate the efficiency of the proposed method.