Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions

This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.