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

Abstract

AbstractFor 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. Numer Methods Partial Differential Eq 28:476–491, 2012