High Degree Immersed Finite Element Spaces by a Least Squares Method

Abstract

We present a least squares framework for constructing $p$-th degree immersed finite element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation enforces interface jump conditions including extended ones already proposed in the literature, and it guarantees the existence of $p$-th IFE shape functions on interface elements. The uniqueness of the proposed $p$-th degree IFE shape functions is also discussed. Computational results are presented to demonstrate the approximation capabilities of the proposed $p$-th IFE spaces as well as other features.