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

共 50 条

[21] On the finite element solution of the pure Neumann problem
Bochev, P
Lehoucq, RB
SIAM REVIEW, 2005, 47 (01) : 50 - 66
[22] Multiscale Finite Element Methods for Flows on Rough Surfaces
Efendiev, Yalchin
Galvis, Juan
Pauletti, M. Sebastian
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (04) : 979 - 1000
[23] Grid adaptation for the Dirichlet-Neumann representation method and the multiscale mixed finite-element method
Lie, Knut-Andreas
Natvig, Jostein R.
Krogstad, Stein
Yang, Yahan
Wu, Xiao-Hui
COMPUTATIONAL GEOSCIENCES, 2014, 18 (3-4) : 357 - 372
[24] Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media
Tyrylgin, Aleksei
Vasilyeva, Maria
Spiridonov, Denis
Chung, Eric T.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 374
[25] A variational multiscale stabilized finite element method for the Stokes flow problem
Liu, XH
Li, SF
FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2006, 42 (07) : 580 - 591
[26] Generalized Multiscale Finite Element Method for piezoelectric problem in heterogeneous media
Ammosov, Dmitry
Vasilyeva, Maria
Nasedkin, Andrey
Efendiev, Yalchin
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2022, 135 : 12 - 25
[27] Generalized Multiscale Finite Element Method for scattering problem in heterogeneous media
Kalachikova, Uygulaana
Vasilyeva, Maria
Harris, Isaac
Chung, Eric T.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 424
[28] A balancing Neumann-Neumann method for a mortar finite element discretization of a fourth order elliptic problem
Marcinkowski, L.
JOURNAL OF NUMERICAL MATHEMATICS, 2010, 18 (03) : 219 - 234
[29] A MULTISCALE FINITE ELEMENT METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS POSED IN DOMAINS WITH ROUGH BOUNDARIES
Madureira, Alexandre L.
MATHEMATICS OF COMPUTATION, 2009, 78 (265) : 25 - 34
[30] Finite element approximation of the pure Neumann problem using the iterative penalty method
Dai, Xiaoxia
APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (02) : 1367 - 1373

← 1 2 3 4 5 →