A study of high-order immersed finite element spaces by pointwise interface conditions on curved interfaces

Abstract

We present a study of p -th degree immersed finite element (IFE) spaces based on pointwise interface conditions that lead to optimal convergence rates for typical second-order elliptic interface problems on interface-independent meshes. We study the existence and approximation properties of IFE spaces spanned by functions that satisfy the extended interface conditions in a pointwise manner on general curved interfaces. We present computational results to demonstrate the approximation capabilities of the proposed IFE spaces.