Convergence rate of multiscale finite element method for various boundary problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:374

Article

Ye, Changqing^1,2  Dong, Hao³  Cui, Junzhi¹ 

[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Xidian Univ, Sch Math & Stat, Xian 710071, Peoples R China

关键词: Multiscale finite element method;    Boundary problems;    Hemivariational inequality;    Homogenization theory;    Numerical convergence rate;   

DOI  :  10.1016/j.cam.2020.112754

来源: Elsevier

【 摘 要 】

In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called boundary correctors is a common technique in existing methods to prove the convergence rate of MsFEM, while we think not reflects the essence of those problems. Instead, we focus on the first-order expansion structure. Through recently developed estimations in homogenization theory, our convergence rate is provided with milder assumptions and in neat forms. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free