A Numerical Method for Solving Two-Dimensional Elliptic Interface Problems with Nonhomogeneous Flux Jump Condition and Nonlinear Jump Condition

被引：1
|
作者：
Wang, Liqun [2 ]
Hou, Songming [3 ]
Shi, Liwei [1 ]
机构：
[1] China Univ Polit Sci & Law, Dept Sci & Technol Teaching, Beijing 102249, Peoples R China
[2] China Univ Petr, Dept Math, Coll Sci, Beijing 102249, Peoples R China
[3] Louisiana Tech Univ, Dept Math & Stat, Ruston, LA 71272 USA
来源：
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2017年 / 18卷 / 3-4期
关键词：
finite element method; elliptic equation; two-dimensional interface problems; nonlinear jump conditions; FINITE-ELEMENT METHODS; DISCONTINUOUS COEFFICIENTS; MATCHED INTERFACE; EQUATIONS; FORMULATION;
D O I：
10.1515/ijnsns-2016-0101
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we propose a new method for solving two-dimensional elliptic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The method we used is traditional finite element method coupled with Newton's method, it is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the L-infinity norm.
引用
收藏
页码：245 / 254
页数：10
相关论文
共 50 条
  • [1] A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions
    Wang, Liqun
    Hou, Songming
    Shi, Liwei
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2018, 10 (03) : 752 - 766
  • [2] On an interface problem with a nonlinear jump condition, numerical approximation of solutions
    Hetzer, G.
    Meir, A. J.
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2007, 4 (3-4) : 519 - 530
  • [3] On some elliptic interface problems with nonhomogeneous jump conditions
    Bhaskar, T. Gnana
    Perera, Kanishka
    ADVANCES IN NONLINEAR ANALYSIS, 2013, 2 (02) : 195 - 211
  • [4] A FINITE DIFFERENCE METHOD FOR ELLIPTIC PROBLEMS WITH IMPLICIT JUMP CONDITION
    Cao, Fujun
    Yuan, Dongfang
    Sheng, Zhiqiang
    Yuan, Guangwei
    He, Limin
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2022, 19 (04) : 439 - 457
  • [5] A jump condition capturing finite difference scheme for elliptic interface problems
    Wang, WC
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2004, 25 (05): : 1479 - 1496
  • [6] A Simple FEM for Solving Two-Dimensional Diffusion Equation with Nonlinear Interface Jump Conditions
    Wang, Liqun
    Hou, Songming
    Shi, Liwei
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2019, 119 (01): : 73 - 90
  • [7] Immersed finite element method of lines for moving interface problems with nonhomogeneous flux jump
    Lin, Tao
    Lin, Yanping
    Zhang, Xu
    RECENT ADVANCES IN SCIENTIFIC COMPUTING AND APPLICATIONS, 2013, 586 : 257 - +
  • [8] Solving elliptic interface problems with jump conditions on Cartesian grids
    Bochkov, Daniil
    Gibou, Frederic
    JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 407
  • [9] A High Order Accurate Numerical Method for Solving Two-Dimensional Dual-Phase-Lagging Equation with Temperature Jump Boundary Condition in Nanoheat Conduction
    Sun, Hong
    Du, Rui
    Dai, Weizhong
    Sun, Zhi-zhong
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2015, 31 (06) : 1742 - 1768
  • [10] Elliptic problems with nonhomogeneous boundary condition and derivatives of nonlinear terms
    Motreanu, Dumitru
    Motreanu, Viorica V.
    BOUNDARY VALUE PROBLEMS, 2014,
12345