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Volume 17, Issue 3
Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem

Na Zhu & Hongxing Rui

Adv. Appl. Math. Mech., 17 (2025), pp. 909-921.

Published online: 2025-03

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  • Abstract

In this paper, we develop an immersed Petrov-Galerkin finite element method for solving two-dimensional Stokes interface problems. The proposed method do not require the solution mesh to align with the fluid interface. We utilize the iso$P_2-P_0$ element, which adopts piecewise linear approximation for velocity on fine elements and piecewise constant approximation for pressure on coarse elements. The vector-valued solution map is constructed to approximate the velocity and pressure based on the jump conditions across the interface. Several numerical experiments demonstrate that the proposed method maintain the optimal convergence rate in the $L_2$-norm and the $H_1$-norm for the velocity and the $L_2$-norm for the pressure.

  • AMS Subject Headings

65N30, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-909, author = {Zhu , Na and Rui , Hongxing}, title = {Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {3}, pages = {909--921}, abstract = {

In this paper, we develop an immersed Petrov-Galerkin finite element method for solving two-dimensional Stokes interface problems. The proposed method do not require the solution mesh to align with the fluid interface. We utilize the iso$P_2-P_0$ element, which adopts piecewise linear approximation for velocity on fine elements and piecewise constant approximation for pressure on coarse elements. The vector-valued solution map is constructed to approximate the velocity and pressure based on the jump conditions across the interface. Several numerical experiments demonstrate that the proposed method maintain the optimal convergence rate in the $L_2$-norm and the $H_1$-norm for the velocity and the $L_2$-norm for the pressure.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0268}, url = {http://global-sci.org/intro/article_detail/aamm/23903.html} }
TY - JOUR T1 - Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem AU - Zhu , Na AU - Rui , Hongxing JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 909 EP - 921 PY - 2025 DA - 2025/03 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2022-0268 UR - https://global-sci.org/intro/article_detail/aamm/23903.html KW - Two-phase flow, discontinuous viscosity, immersed FEM. AB -

In this paper, we develop an immersed Petrov-Galerkin finite element method for solving two-dimensional Stokes interface problems. The proposed method do not require the solution mesh to align with the fluid interface. We utilize the iso$P_2-P_0$ element, which adopts piecewise linear approximation for velocity on fine elements and piecewise constant approximation for pressure on coarse elements. The vector-valued solution map is constructed to approximate the velocity and pressure based on the jump conditions across the interface. Several numerical experiments demonstrate that the proposed method maintain the optimal convergence rate in the $L_2$-norm and the $H_1$-norm for the velocity and the $L_2$-norm for the pressure.

Zhu , Na and Rui , Hongxing. (2025). Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem. Advances in Applied Mathematics and Mechanics. 17 (3). 909-921. doi:10.4208/aamm.OA-2022-0268
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