Robust a posteriori error estimators with error-dominated oscillation for the reaction-diffusion equation

Abstract: We apply the recent approach of C. Kreuzer and A. Veeser to derive a robust a posteriori error estimator for the reaction-diffusion equation. The estimator together with the corresponding oscillation yields global upper and local lower bounds for the error in the energy norm, and the involved constants do not depend on the ratio of reaction to diffusion. In particular the new oscillation is also bounded by the error in a robust way.