Recovery-Based A Posteriori Error Estimation For Elliptic Interface Problems Based On Immersed Finite Element Methods

This paper develops a recovery-based a posteriori error estimation for elliptic interface problems based on partially penalized immersed finite element methods.First,we construct a new gradient recovery method,which applies superconvergent cluster recovery operator on each subdomain and weighted average operator at recovering points on the approximated interface.Then it is proved that the recovered gradient superconverges to the exact gradient at the rate of O(h^1.5).Consequently,the proposed method gives an asymptotically exact a posteriori error estimator for the partially penalized immersed finite element methods and the adaptive algorithm.Numerical examples show that the error estimator and the corre-sponding adaptive algorithm are both reliable and e cient.