A mixed immersed finite element method for fourth-order interface problems on surfaces

This paper presents the first numerical attempt on fourth-order interface problems on surfaces. A mixed immersed surface finite element method based on Ciarlet-Raviart formulation is proposed for solving the problem with three types of boundary conditions. One important advantage of this method is that it can avoid the generation of complex body-fitting surface meshes. The immersed surface finite element space is given based on the mixed formulation. By modifying the representation of numerical solutions, the method is extended to solve the fourth-order interface problem with nonhomogeneous flux jump conditions. Numerical examples are given to illustrate the capabilities of the proposed method.