A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces

<p style='text-indent:20px;'>In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements one velocity component and non-conforming the other component. pressure is approximated by piecewise constant. Unisolvency, among fundamental properties of vector-valued functions, analyzed. Based on spaces, semi-discrete full-discrete schemes are developed solving equations stationary or moving interface. Re-meshing not required in our numerical scheme moving-interface problem. Numerical experiments carried out to demonstrate performance method.</p>