A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions

被引：20

作者：

Ji, Haifeng ^{[1
]}

Zhang, Qian ^{[2
]}

Wang, Qiuliang ^{[3
]}

Xie, Yifan ^{[4
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Sch Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Nanjing Univ Chinese Med, Inst Informat Technol, Nanjing 210023, Jiangsu, Peoples R China

[3] Shangqiu Normal Univ, Sch Math & Stat, Shangqiu 476000, Henan, Peoples R China

[4] Nanjing Univ, Sch Earth Sci & Engn, Nanjing 210023, Jiangsu, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2018年 / 8卷 / 01期

基金：

美国国家科学基金会; 中国博士后科学基金;

关键词：

Immersed finite element method; interface problem; Cartesian mesh; non-homogeneous jump condition; closest-point projection; BOUNDARY INTEGRAL METHOD; DISCONTINUOUS COEFFICIENTS; IRREGULAR DOMAINS; MATCHED INTERFACE; SINGULAR SOURCES; EQUATIONS; APPROXIMATION; FORMULATION;

D O I：

10.4208/eajam.160217.070717a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A partially penalised immersed finite element method for interface problems with discontinuous coefficients and non-homogeneous jump conditions based on unfitted meshes independent of the interface is proposed. The arising systems of linear equations have symmetric positive definite matrices which allows the use of fast solvers and existing codes. Optimal error estimates in an energy norm are derived. Numerical examples demonstrate the efficiency of the method.

引用

页码：1 / 23

页数：23

共 41 条

[1] A Partially Penalty Immersed Interface Finite Element Method for Anisotropic Elliptic Interface Problems [J].

An, Na ;

Chen, Huan-zhen .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (06) :1984-2028

[2] A second order virtual node method for elliptic problems with interfaces and irregular domains [J].

Bedrossian, Jacob ;

von Brecht, James H. ;

Zhu, Siwei ;

Sifakis, Eftychios ;

Teran, Joseph M. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (18) :6405-6426

[3] Discontinuous bubble scheme for elliptic problems with jumps in the solution [J].

Chang, Kwang S. ;

Kwak, D. Y. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (5-8) :494-508

[4] A coupling interface method for elliptic interface problems [J].

Chern, I-Liang ;

Shu, Yu-Chen .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :2138-2174

[5] NUMERICAL APPROXIMATION OF INTERNAL DISCONTINUITY INTERFACE PROBLEMS [J].

Discacciati, Marco ;

Quarteroni, Alfio ;

Quinodoz, Samuel .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2013, 35 (05) :A2341-A2369

[6] The extended/generalized finite element method: An overview of the method and its applications [J].

Fries, Thomas-Peter ;

Belytschko, Ted .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 84 (03) :253-304

[7] Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions [J].

Gong, Yan ;

Li, Bo ;

Li, Zhilin .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (01) :472-495

[8] An unfitted finite element method, based on Nitsche's method, for elliptic interface problems [J].

Hansbo, A ;

Hansbo, P .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (47-48) :5537-5552

[9] The Convergence of the Bilinear and Linear Immersed Finite Element Solutions to Interface Problems [J].

He, Xiaoming ;

Lin, Tao ;

Lin, Yanping .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (01) :312-330

[10]

He XM, 2011, INT J NUMER ANAL MOD, V8, P284

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