Volume 11, Issue 5
An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points

Yuan Chen, Songming Hou & Xu Zhang

Adv. Appl. Math. Mech., 11 (2019), pp. 1005-1021.

Published online: 2019-06

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  • Abstract

Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface problems. We follow the idea of immersed finite element by modifying local basis functions to accommodate interface conditions. We enrich the local finite element space by adding new basis functions for handling non-homogeneous flux jump. The numerical scheme is symmetric and positive definite. Numerical experiments are provided to demonstrate the features of our method.

  • Keywords

Immersed finite element, interface problems, triple junction, multi-domain.

  • AMS Subject Headings

35R05, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-1005, author = {}, title = {An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {1005--1021}, abstract = {

Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface problems. We follow the idea of immersed finite element by modifying local basis functions to accommodate interface conditions. We enrich the local finite element space by adding new basis functions for handling non-homogeneous flux jump. The numerical scheme is symmetric and positive definite. Numerical experiments are provided to demonstrate the features of our method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0175}, url = {http://global-sci.org/intro/article_detail/aamm/13198.html} }
TY - JOUR T1 - An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1005 EP - 1021 PY - 2019 DA - 2019/06 SN - 11 DO - http://dor.org/10.4208/aamm.OA-2018-0175 UR - https://global-sci.org/intro/article_detail/aamm/13198.html KW - Immersed finite element, interface problems, triple junction, multi-domain. AB -

Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface problems. We follow the idea of immersed finite element by modifying local basis functions to accommodate interface conditions. We enrich the local finite element space by adding new basis functions for handling non-homogeneous flux jump. The numerical scheme is symmetric and positive definite. Numerical experiments are provided to demonstrate the features of our method.

Yuan Chen, Songming Hou & Xu Zhang. (2019). An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points. Advances in Applied Mathematics and Mechanics. 11 (5). 1005-1021. doi:10.4208/aamm.OA-2018-0175
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