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

共 50 条

[31] A modified scaled boundary finite-element method for problems with parallel side-faces. Part II. Application and evaluation
Li, Boning
Cheng, Liang
Deeks, Andrew J.
Teng, Bin
APPLIED OCEAN RESEARCH, 2005, 27 (4-5) : 224 - 234
[32] Error Analysis of the Nonconforming P1 Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations
Yanming Lai
Kewei Liang
Ping Lin
Xiliang Lu
Qimeng Quan
AnnalsofAppliedMathematics, 2024, 40 (01) : 43 - 70
[33] Special-purpose elements to impose Periodic Boundary Conditions for multiscale computational homogenization of composite materials with the explicit Finite Element Method
Sadaba, S.
Herraez, M.
Naya, F.
Gonzalez, C.
Llorca, J.
Lopes, C. S.
COMPOSITE STRUCTURES, 2019, 208 : 434 - 441
[34] Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites
Jacques, S.
De Baere, I.
Van Paepegem, W.
COMPOSITES SCIENCE AND TECHNOLOGY, 2014, 92 : 41 - 54
[35] The P2.5D finite element method for periodic structures in half-space soil with application to periodic pile rows
Lu, Jian-Fei
Chen, Kuan-Kuan
Feng, Qing-Song
COMPUTERS AND GEOTECHNICS, 2023, 164
[36] About solution of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. part 2: boundary conditions
Lyakhovich, Leonid
Negrozov, Oleg
RSP 2017 - XXVI R-S-P SEMINAR 2017 THEORETICAL FOUNDATION OF CIVIL ENGINEERING, 2017, 117
[37] Solution of three-dimensional boundary layer equations by a discontinuous finite element method. Part II. Implementation and numerical results
Caussignac, Phillippe, 1600, (79):
[38] Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spaces -: Part II.: Optimal rate of convergence of the p-version finite element solutions
Babuska, I
Guo, BQ
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (05): : 689 - 719
[39] A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals
Wang, Liqun
Zheng, Hui
Lu, Xin
Shi, Liwei
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 393 : 117 - 138
[40] Analysis of a P1⊕ RT0 finite element method for linear elasticity with Dirichlet and mixed boundary conditions
Li, Hongpeng
Li, Xu
Rui, Hongxing
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2024, 50 (01)

← 1 2 3 4 5 →