Three-dimensional immersed finite element method for second-order elliptic interface problems

In this paper we develop an immersed finite element method for the elliptic interface problems in three-dimensional space. The method is based on linear polynomials on non-interface tetrahedral elements and piecewise linear polynomials on interface tetrahedral elements. Optimal-order error estimates for the interpolation of a function in the usual Sobolev space are derived by using the multipoint Taylor expansion technique. It shows that the 3-D IFE space has approximation capability similar to that of the standard linear finite element space.