Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems
Numerical Analysis
2020-02-06 v3 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.1908.08698,
title = {Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems},
author = {Changqing Ye and Hao Dong and Junzhi Cui},
journal= {arXiv preprint arXiv:1908.08698},
year = {2020}
}