A Petrov–Galerkin immersed finite element method for steady Navier–Stokes interface problem with non-homogeneous jump conditions

Abstract

This paper develops a lowest-order Petrov–Galerkin immersed Q1−Q0 method for solving Stokes interface problem. We make use of a uniform, interface-unfitted Cartesian mesh. An immersed Petrov–Galerkin formulation is presented, where the test spaces are conventional finite element spaces and the solution spaces satisfying the jump conditions. For the Stokes and Navier–Stokes interface problem, simple stabilized items are introduced. The nonlinear convective term is treated using Picard’s iteration. Extensive numerical experiments validate the feasibility and optimal convergence order for the Petrov–Galerkin immersed Q1−Q0 scheme both with homogeneous and non-homogeneous jumps.