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

Liqun Wang, Songming Hou & Liwei Shi

DOI: 10.4208/jcm.1309-m4207

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

Published online: 2014-02

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  • 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

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  • 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, Sharp-edged interface, Jump condition, 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 and Liwei Shi. (2014). 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
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