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Volume 18, Issue 1
A $P_2$-$P_1$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problems

Yuan Chen & Xu Zhang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 120-141.

Published online: 2021-02

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  • Abstract

In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The $P_2$-$P_1$ local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems. Penalty terms are imposed on both interface edges and the actual interface curves. Ghost penalty terms are enforced to enhance the stability of the numerical scheme, especially for the pressure approximation. Optimal convergences are observed in various numerical experiments with different interface shapes and coefficient configurations. The effects of the ghost penalty and the fictitious element are also examined through numerical experiments.

  • Keywords

Stokes interface problem, immersed finite element method, fictitious element, least-squares.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-120, author = {Yuan and Chen and and 10377 and and Yuan Chen and Xu and Zhang and and 10379 and and Xu Zhang}, title = {A $P_2$-$P_1$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {1}, pages = {120--141}, abstract = {

In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The $P_2$-$P_1$ local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems. Penalty terms are imposed on both interface edges and the actual interface curves. Ghost penalty terms are enforced to enhance the stability of the numerical scheme, especially for the pressure approximation. Optimal convergences are observed in various numerical experiments with different interface shapes and coefficient configurations. The effects of the ghost penalty and the fictitious element are also examined through numerical experiments.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18624.html} }
TY - JOUR T1 - A $P_2$-$P_1$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problems AU - Chen , Yuan AU - Zhang , Xu JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 120 EP - 141 PY - 2021 DA - 2021/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18624.html KW - Stokes interface problem, immersed finite element method, fictitious element, least-squares. AB -

In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The $P_2$-$P_1$ local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems. Penalty terms are imposed on both interface edges and the actual interface curves. Ghost penalty terms are enforced to enhance the stability of the numerical scheme, especially for the pressure approximation. Optimal convergences are observed in various numerical experiments with different interface shapes and coefficient configurations. The effects of the ghost penalty and the fictitious element are also examined through numerical experiments.

Yuan Chen & Xu Zhang. (2021). A $P_2$-$P_1$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problems. International Journal of Numerical Analysis and Modeling. 18 (1). 120-141. doi:
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