In this paper, we develop a new unfitted finite element method for the Stokes interface problem. In this method, the velocity is approximated using a piecewise linear continuous Galerkin element enriched by the lowest-order Raviart–Thomas element, while the pressure is approximated using a piecewise constant element. To construct a stable solver with an optimal convergence rate, we adopt cut finite element strategies and add ghost penalty terms for both velocity and pressure. We numerically show that the considered method achieves an optimal convergence rate as well as preserving the divergence constraint. Several benchmark problems are presented to test its stability, divergence property, and convergence performance, demonstrating the desired pressure and viscosity robustness in complex geometries, thereby outperforming other numerical methods.
Citation: Kun Wang, Lin Mu. Numerical investigation of a new cut finite element method for Stokes interface equations[J]. Electronic Research Archive, 2025, 33(4): 2503-2524. doi: 10.3934/era.2025111
In this paper, we develop a new unfitted finite element method for the Stokes interface problem. In this method, the velocity is approximated using a piecewise linear continuous Galerkin element enriched by the lowest-order Raviart–Thomas element, while the pressure is approximated using a piecewise constant element. To construct a stable solver with an optimal convergence rate, we adopt cut finite element strategies and add ghost penalty terms for both velocity and pressure. We numerically show that the considered method achieves an optimal convergence rate as well as preserving the divergence constraint. Several benchmark problems are presented to test its stability, divergence property, and convergence performance, demonstrating the desired pressure and viscosity robustness in complex geometries, thereby outperforming other numerical methods.
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Kun Wang, Lin Mu. Numerical investigation of a new cut finite element method for Stokes interface equations[J]. Electronic Research Archive, 2025, 33(4): 2503-2524. doi: 10.3934/era.2025111
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