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Licensed Unlicensed Requires Authentication Published by De Gruyter April 27, 2023

A New Immersed Finite Element Method for Two-Phase Stokes Problems Having Discontinuous Pressure

  • Gwanghyun Jo ORCID logo and Do Young Kwak ORCID logo EMAIL logo

Abstract

In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements. On the noninterface element, the standard Crouzeix–Raviart element and the P 0 element pair is used. On the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken P 1 -nonconforming finite element method for interface problems, SIAM J. Numer. Anal. (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different. There are two kinds of basis functions. The first kind of basis satisfies the Laplace–Young condition under the assumption of the continuity of the pressure variable. In the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace–Young condition. We remark that in the second kind the pressure variable has two degrees of freedom on each interface element. Therefore, our methods can handle the discontinuous pressure case. Numerical results including the case of the discontinuous pressure variable are provided. We see optimal convergence orders for all examples.

MSC 2020: 65N30; 76D05; 76D07

Award Identifier / Grant number: 2020R1C1C1A01005396

Award Identifier / Grant number: 2021R1A2C1003340

Funding statement: The first author is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01005396). The second author is supported by NRF funded by MSIT (No. 2021R1A2C1003340).

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Received: 2022-06-09
Revised: 2022-12-13
Accepted: 2023-03-01
Published Online: 2023-04-27
Published in Print: 2024-01-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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