An enriched cut finite element method for Stokes interface equations

Kun Wang and Lin Mu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 218, issue C, 644-665

Abstract: In this paper, we consider an enriched cut finite element method (ECFEM) with interface-unfitted meshes for solving Stokes interface equations consisting of two incompressible fluids with different viscosities. By approximating the velocity with the enriched P1 element and the pressure with the P0 element, and stabilizing the Galerkin variational formulation with suitable ghost penalty terms, we propose the new ECFEM and prove that it is well-posed and has the optimal a priori error estimate in the energy norm. All derived results are independent of the interface position. Moreover, compared with other conforming finite element methods with the optimal rate in convergence, the proposed scheme here not only has the minimum degrees of freedom, but also avoids using the derivative of the pressure in the penalty term. The presented numerical examples validate the theoretical predictions.

Keywords: Stokes interface equations; Cut finite element method; Enriched finite element method; Interface-unfitted mesh; Lowest order element (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:218:y:2024:i:c:p:644-665

DOI: 10.1016/j.matcom.2023.12.016

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