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Volume 27, Issue 4
An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients

Hua Wang, Jinru Chen, Pengtao Sun & Rihui Lan

DOI: 10.4208/cicp.OA-2019-0021

Commun. Comput. Phys., 27 (2020), pp. 1174-1200.

Published online: 2020-02

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  • Abstract

In this paper, a conforming enriched finite element method over an interface-unfitted mesh is developed and analyzed for a type of Stokes-elliptic interface problem with jump coefficients. An inf-sup stability result that is uniform with respect to the mesh size is proved in order to derive the corresponding well-posedness and optimal convergence properties in spite of the low regularity of the problem. The developed new finite element method breaks the limit of the classical immersed finite element method (IFEM) which can only deal with the case of identical governing equations on either side of the interface. Numerical experiments are carried out to validate the theoretical results. This is the first step of our new method to solve complex interface problems with different governing equations on either side of the interface, and will be extended to solve transient interface problems towards fluid-structure interaction problems in the future.

  • Keywords

Conforming enriched finite element, interface-unfitted mesh, Stokes-elliptic interface problem, inf-sup condition, optimal convergence.

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wanghua.math@foxmail.com (Hua Wang)

jrchen@njnu.edu.cn (Jinru Chen)

pengtao.sun@unlv.edu (Pengtao Sun)

lanr1@unlv.nevada.edu (Rihui Lan)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1174, author = {Wang , HuaChen , JinruSun , Pengtao and Lan , Rihui}, title = {An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {1174--1200}, abstract = {

In this paper, a conforming enriched finite element method over an interface-unfitted mesh is developed and analyzed for a type of Stokes-elliptic interface problem with jump coefficients. An inf-sup stability result that is uniform with respect to the mesh size is proved in order to derive the corresponding well-posedness and optimal convergence properties in spite of the low regularity of the problem. The developed new finite element method breaks the limit of the classical immersed finite element method (IFEM) which can only deal with the case of identical governing equations on either side of the interface. Numerical experiments are carried out to validate the theoretical results. This is the first step of our new method to solve complex interface problems with different governing equations on either side of the interface, and will be extended to solve transient interface problems towards fluid-structure interaction problems in the future.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0021}, url = {http://global-sci.org/intro/article_detail/cicp/14847.html} }
TY - JOUR T1 - An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients AU - Wang , Hua AU - Chen , Jinru AU - Sun , Pengtao AU - Lan , Rihui JO - Communications in Computational Physics VL - 4 SP - 1174 EP - 1200 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0021 UR - https://global-sci.org/intro/article_detail/cicp/14847.html KW - Conforming enriched finite element, interface-unfitted mesh, Stokes-elliptic interface problem, inf-sup condition, optimal convergence. AB -

In this paper, a conforming enriched finite element method over an interface-unfitted mesh is developed and analyzed for a type of Stokes-elliptic interface problem with jump coefficients. An inf-sup stability result that is uniform with respect to the mesh size is proved in order to derive the corresponding well-posedness and optimal convergence properties in spite of the low regularity of the problem. The developed new finite element method breaks the limit of the classical immersed finite element method (IFEM) which can only deal with the case of identical governing equations on either side of the interface. Numerical experiments are carried out to validate the theoretical results. This is the first step of our new method to solve complex interface problems with different governing equations on either side of the interface, and will be extended to solve transient interface problems towards fluid-structure interaction problems in the future.

Wang , HuaChen , JinruSun , Pengtao and Lan , Rihui. (2020). An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients. Communications in Computational Physics. 27 (4). 1174-1200. doi:10.4208/cicp.OA-2019-0021
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