The paper proposes a Petrov–Galerkin immersed finite element (PGIFE) method for solving Stokes interface problems. We employ the uniform mesh which is independent of interface. Immersed \(P_1\) and \(P_0\) spaces for velocity and pressure are constructed according to the jump conditions. We enrich the velocity space by the lowest RT0 element to ensure the inf-sup stability. The PGIFE method we developed yields the global divergence-free velocity and pressure-robustness. The existence and uniqueness of the approximated solution are derived. We obtain the optimal error estimate and prove that the error estimate for velocity is independent of pressure. Numerical experiments validate the optimal convergence results and the robustness of our method.
