Residual-based a posteriori error estimation for immersed finite element methods

TL;DR

This paper develops a residual-based a posteriori error estimator for immersed finite element methods solving elliptic interface problems, demonstrating its reliability, efficiency, and robustness regardless of interface position or coefficient contrast.

Contribution

It introduces a new a posteriori error estimation technique for immersed finite element methods that is proven to be reliable and efficient, independent of interface location.

Findings

Error estimator is reliable and efficient

Constant is independent of interface position

Method is robust against coefficient contrast

Abstract

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally utilized on interface-unfitted meshes. Our a posteriori error estimate is proved to be both reliable and efficient with reliability constant independent of the location of the interface. Numerical results indicate that the efficiency constant is independent of the interface location and that the error estimation is robust with respect to the coefficient contrast.