Year: 2014
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 39–57
Abstract
We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid are considered. Both Dirichlet and Neumann boundary conditions are discussed. The coefficient matrix data can be given only on the grids, rather than an analytical function. Extensive numerical experiments show that this method is second order accurate in the $L^∞$ norm.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1309-m4207
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 39–57
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Elliptic equation Sharp-edged interface Jump condition Matrix coefficient.
-
Gradient preserved method for solving heat conduction equation with variable coefficients in double layers
Bora, Aniruddha | Dai, WeizhongApplied Mathematics and Computation, Vol. 386 (2020), Iss. P.125516
https://doi.org/10.1016/j.amc.2020.125516 [Citations: 2] -
Accurate gradient preserved method for solving heat conduction equations in double layers
Yan, Yun | Dai, Weizhong | Wu, Longyuan | Zhai, ShuyingApplied Mathematics and Computation, Vol. 354 (2019), Iss. P.58
https://doi.org/10.1016/j.amc.2019.02.038 [Citations: 2] -
A simple method for matrix-valued coefficient elliptic equations with sharp-edged interfaces
Wang, Liqun | Shi, LiweiApplied Mathematics and Computation, Vol. 242 (2014), Iss. P.917
https://doi.org/10.1016/j.amc.2014.06.084 [Citations: 1] -
A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces
Wang, Liqun | Shi, LiweiNumerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 4 P.475
https://doi.org/10.4208/nmtma.2015.m1331 [Citations: 0] -
A simple weak formulation for solving two-dimensional diffusion equation with local reaction on the interface
Wang, Liqun | Hou, Songming | Shi, LiweiComputers & Mathematics with Applications, Vol. 75 (2018), Iss. 4 P.1378
https://doi.org/10.1016/j.camwa.2017.11.003 [Citations: 3] -
A numerical method for solving elasticity equations with interface involving multi-domains and triple junction points
Wang, Liqun | Hou, Songming | Shi, Liwei | Solow, JamesApplied Mathematics and Computation, Vol. 251 (2015), Iss. P.615
https://doi.org/10.1016/j.amc.2014.11.072 [Citations: 2] -
A Numerical Method for Solving Two-Dimensional Elliptic Interface Problems with Nonhomogeneous Flux Jump Condition and Nonlinear Jump Condition
Wang, Liqun | Hou, Songming | Shi, LiweiInternational Journal of Nonlinear Sciences and Numerical Simulation, Vol. 18 (2017), Iss. 3-4 P.245
https://doi.org/10.1515/ijnsns-2016-0101 [Citations: 0] -
Numerical analysis of interface hybrid difference methods for elliptic interface equations
Jeon, Youngmok | Tran, Mai LanJournal of Computational and Applied Mathematics, Vol. 377 (2020), Iss. P.112869
https://doi.org/10.1016/j.cam.2020.112869 [Citations: 1] -
An improved non-traditional finite element formulation for solving three-dimensional elliptic interface problems
Wang, Liqun | Hou, Songming | Shi, LiweiComputers & Mathematics with Applications, Vol. 73 (2017), Iss. 3 P.374
https://doi.org/10.1016/j.camwa.2016.11.035 [Citations: 8]