An immersed discontinuous finite element method for Stokes interface problems

Abstract We present a discontinuous immersed finite element (IFE) method for Stokes interface problems on Cartesian meshes that do not require the mesh to be aligned with the interface. As such, the method allows unfitted meshes with elements cut by the interface and thus, may contain more than one fluid. On these unfitted meshes we construct an immersed Q 1 / Q 0 finite element space according to the location of the interface and pertinent interface jump conditions. The proposed Q 1 / Q 0 IFE shape functions have several desirable features such as the unisolvence and the partition of unity. We present several numerical examples to demonstrate that the proposed IFE spaces maintain the optimal approximation capability with respect to the polynomials used. We also show that related discontinuous IFE solutions of Stokes interface problems maintain the optimal convergence rates in both L 2 and broken H 1 norms.

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