A note on the immersed finite element basis functions for elliptic interface problems

Abstract This paper considers the structure of basis functions in the bilinear immersed finite element space for two dimensional elliptic interface problems. On a rectangular interface element, each immersed basis function can be decomposed into a standard bilinear basis function and a corresponding bubble function, which provides another perspective on the nature of immersed basis functions. Detailed expressions of these bubble functions are presented on the reference element. The same pattern can be carried out for other immersed finite element spaces in a similar manner.