Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, we develop an immersed Petrov-Galerkin finite elementmethod for solving two-dimensional Stokes interface problems. The proposed methoddo 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 elementsand piecewise constant approximation for pressure on coarse elements. The vector-valued solution map is constructed to approximate the velocity and pressure based onthe jump conditions across the interface. Several numerical experiments demonstratethat the proposed method maintain the optimal convergence rate in the $L_2$-norm andthe $H_1$-norm for the velocity and the $L_2$-norm for the pressure.