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Volume 8, Issue 1
A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions

Haifeng Ji, Qian Zhang, Qiuliang Wang & Yifan Xie

DOI: 10.4208/eajam.160217.070717a

East Asian J. Appl. Math., 8 (2018), pp. 1-23.

Published online: 2018-02

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  • Abstract

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.

  • Keywords

Immersed finite element method, interface problem, Cartesian mesh, non-homogeneous jump condition, closest-point projection.

  • AMS Subject Headings

65N15, 65N30, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-1, author = {Haifeng Ji, Qian Zhang, Qiuliang Wang and Yifan Xie}, title = {A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {1}, pages = {1--23}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.160217.070717a}, url = {http://global-sci.org/intro/article_detail/eajam/10915.html} }
TY - JOUR T1 - A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions AU - Haifeng Ji, Qian Zhang, Qiuliang Wang & Yifan Xie JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 23 PY - 2018 DA - 2018/02 SN - 8 DO - http://doi.org/10.4208/eajam.160217.070717a UR - https://global-sci.org/intro/article_detail/eajam/10915.html KW - Immersed finite element method, interface problem, Cartesian mesh, non-homogeneous jump condition, closest-point projection. AB -

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.

Haifeng Ji, Qian Zhang, Qiuliang Wang and Yifan Xie. (2018). A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions. East Asian Journal on Applied Mathematics. 8 (1). 1-23. doi:10.4208/eajam.160217.070717a
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