Higher degree immersed finite element spaces constructed according to the actual interface

We discuss the construction of higher degree immersed finite element (IFE) spaces that can be used to solve two dimensional second order elliptic interface problems having general interfaces without requiring the mesh to be aligned with the material interfaces. The optimal approximation capability of the proposed piecewise pth degree IFE spaces are demonstrated by numerical experiments with interpolations. Numerical solutions to interface problems generated from a partially penalized method based on the proposed higher order IFE spaces also suggest optimal convergence in both the L2 and H1 norms under mesh refinement.