Year: 2021
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18624
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 120–141
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stokes interface problem immersed finite element method fictitious element least-squares.