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arXiv · 1908.08698

Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems

Changqing Ye·Hao Dong·Junzhi Cui
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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.

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Changqing Ye, Hao Dong, Junzhi Cui. 2019-08-23. Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems. https://doi.org/10.1016/j.cam.2020.112754

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