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

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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper explores the structure of basis functions in the bilinear immersed finite element space for two dimensional elliptic interface problems, demonstrating that each immersed basis function on a rectangular interface element can be broken down into a standard bilinear basis function and a corresponding bubble function. By providing detailed expressions of these bubble functions on the reference element, it reveals another perspective on the nature of immersed basis functions, which can be extended to other immersed finite element spaces in a similar manner.