Volume 32, Issue 1
An Improved Non-Traditional Finite Element Formulation for Solving the Elliptic Interface Problems

Liqun Wang, Songming Hou & Liwei Shi

J. Comp. Math., 32 (2014), pp. 39-57.

Published online: 2014-02

Preview Full PDF 601 2615
Export citation
  • 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.

  • Keywords

Elliptic equation Sharp-edged interface Jump condition Matrix coefficient

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-32-39, author = {Liqun Wang, Songming Hou and Liwei Shi}, title = {An Improved Non-Traditional Finite Element Formulation for Solving the Elliptic Interface Problems}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1309-m4207}, url = {http://global-sci.org/intro/article_detail/jcm/9868.html} }
TY - JOUR T1 - An Improved Non-Traditional Finite Element Formulation for Solving the Elliptic Interface Problems AU - Liqun Wang, Songming Hou & Liwei Shi JO - Journal of Computational Mathematics VL - 1 SP - 39 EP - 57 PY - 2014 DA - 2014/02 SN - 32 DO - http://doi.org/10.4208/jcm.1309-m4207 UR - https://global-sci.org/intro/article_detail/jcm/9868.html KW - Elliptic equation KW - Sharp-edged interface KW - Jump condition KW - Matrix coefficient AB -

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.

Liqun Wang, Songming Hou & Liwei Shi. (1970). An Improved Non-Traditional Finite Element Formulation for Solving the Elliptic Interface Problems. Journal of Computational Mathematics. 32 (1). 39-57. doi:10.4208/jcm.1309-m4207
Copy to clipboard
The citation has been copied to your clipboard