Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps

For elliptic interface problems with flux jumps, this article studies robust residual- and recovery-based a posteriori error estimators for the conforming finite element approximation. The residual estimator is a natural extension of that developed in [Bernardi and Verfürth, Numer Math 85 (2000), 579-608; Petzoldt, Adv Comp Math 16 (2002), 47-75], and the recovery estimator is a nontrivial extension of our method developed in Cai and Zhang, SIAM J Numer Anal 47 (2009) 2132-2156. It is shown theoretically that reliability and efficiency bounds of these error estimators are independent of the jumps provided that the distribution of the coefficients is locally monotone. © 2010 Wiley Periodicals, Inc.