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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@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 KW - uniform grid KW - interface problem KW - Robin type jump KW - 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 & Yunkyong Hyon. (1970). 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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