AN IMMERSED CROUZEIX-RAVIART FINITE ELEMENT METHOD FOR NAVIER-STOKES EQUATIONS WITH MOVING INTERFACES

In this article, we develop a Cartesian-mesh finite element method for solving NavierStokes interface problems with moving interfaces. The spatial discretization uses the immersed Crouzeix-Raviart nonconforming finite element introduced in [29]. A backward Euler full-discrete scheme is developed which embeds Newton's iteration to treat the nonlinear convective term. The proposed IFE method does not require any stabilization terms while maintaining its convergence in optimal order. Numerical experiments with various interface shapes and jump coefficients are provided to demonstrate the accuracy of the proposed method. The numerical results are compared to the analytical solution as well as the standard finite element method with body fitting meshes. Numerical results indicate the optimal order of convergence of the IFE method.