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Volume 14, Issue 4-5
A New Finite Element for Interface Problems Having Robin Type Jump

Do Y. Kwak, Seungwoo Lee & Yunkyong Hyon

Int. J. Numer. Anal. Mod., 14 (2017), pp. 532-549.

Published online: 2017-08

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  • Abstract

We propose a new finite element method for solving second order elliptic interface problems whose solution has a Robin type jump along the interface. We cast the problem into a new variational form and introduce a finite element method to solve it using a uniform grid. We modify the $P_1$-Crouzeix-Raviart element so that the shape functions satisfy the jump conditions along the interface. We note that there are cases that the Lagrange type basis can not be used because of the jump in the value. Numerical experiments are provided.

  • Keywords

Finite element, uniform grid, interface problem, Robin type jump, $P_1$-Crouzeix-Raviart finite element method.

  • AMS Subject Headings

65N15, 65N30, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-14-532, author = {Do Y. Kwak, Seungwoo Lee and Yunkyong Hyon}, title = {A New Finite Element for Interface Problems Having Robin Type Jump}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {532--549}, abstract = {

We propose a new finite element method for solving second order elliptic interface problems whose solution has a Robin type jump along the interface. We cast the problem into a new variational form and introduce a finite element method to solve it using a uniform grid. We modify the $P_1$-Crouzeix-Raviart element so that the shape functions satisfy the jump conditions along the interface. We note that there are cases that the Lagrange type basis can not be used because of the jump in the value. Numerical experiments are provided.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10048.html} }
TY - JOUR T1 - A New Finite Element for Interface Problems Having Robin Type Jump AU - Do Y. Kwak, Seungwoo Lee & Yunkyong Hyon JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 532 EP - 549 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10048.html KW - Finite element, uniform grid, interface problem, Robin type jump, $P_1$-Crouzeix-Raviart finite element method. AB -

We propose a new finite element method for solving second order elliptic interface problems whose solution has a Robin type jump along the interface. We cast the problem into a new variational form and introduce a finite element method to solve it using a uniform grid. We modify the $P_1$-Crouzeix-Raviart element so that the shape functions satisfy the jump conditions along the interface. We note that there are cases that the Lagrange type basis can not be used because of the jump in the value. Numerical experiments are provided.

Do Y. Kwak, Seungwoo Lee and Yunkyong Hyon. (2017). A New Finite Element for Interface Problems Having Robin Type Jump. International Journal of Numerical Analysis and Modeling. 14 (4-5). 532-549. doi:
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