(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
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 isoP_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.