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

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.