P1-nonconforming quadrilateral finite element space with periodic boundary conditions: Part II. Application to the nonconforming heterogeneous multiscale method

被引：1

作者：

Yim, Jaeryun ^{[1
]}

Sheen, Dongwoo ^{[2
,4
]}

Sim, Imbo ^{[3
]}

机构：

[1] Encored Inc, Honolulu, HI USA

[2] Seoul Natl Univ, Dept Math, Seoul, South Korea

[3] Dong A Univ, Dept Mech Engn, Busan, South Korea

[4] Seoul Natl Univ, Dept Math, Seoul 08826, South Korea

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

heterogeneous multiscale method; homogenization; nonconforming finite element method; ELLIPTIC PROBLEMS; STATIONARY STOKES; HOMOGENIZATION; CONVERGENCE; MSFEM;

D O I：

10.1002/num.23009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such process numerically. In this paper we introduce a FEHMM scheme for multiscale elliptic problems based on nonconforming elements. In particular we use the noconforming element with the periodic boundary condition introduced in the companion paper. Theoretical analysis derives a priori error estimates in the standard Sobolev norms. Several numerical results which confirm our analysis are provided.

引用

页码：3309 / 3331

页数：23

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