A MULTISCALE FINITE ELEMENT METHOD FOR OSCILLATING NEUMANN PROBLEM ON ROUGH DOMAIN

被引：4

作者：

Ming, Pingbing ^{[1
]}

Xu, Xianmin ^{[2
]}

机构：

[1] Chinese Acad Sci, Univ Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC,AMSS, 55 Zhong Guan Cun East Rd, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Univ Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC,AMSS,NCMIS, 55 Zhong Guan Cun East Rd, Beijing 100190, Peoples R China

来源：

MULTISCALE MODELING & SIMULATION | 2016年 / 14卷 / 04期

基金：

中国国家自然科学基金;

关键词：

multiscale finite element method; rough boundary; homogenization; NAVIER-STOKES SYSTEM; ELLIPTIC PROBLEMS; COMPLICATED DOMAINS; BOUNDARY; COEFFICIENTS; SURFACE; FLOW; CONVERGENCE; EQUATIONS; MODEL;

D O I：

10.1137/15M1044709

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a new multiscale finite element method for the Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the microscopically geometrical and physical information of the rough boundary. Our approach applies to problems posed on a domain with a rough boundary as well as oscillating boundary conditions. We prove the method has a linear convergence rate in the energy norm with a weak resonance term for periodic roughness. Numerical results are reported for both periodic and nonperiodic roughness.

引用

页码：1276 / 1300

页数：25

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