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We consider the a posteriori error estimation forconvection-diffusion-reaction equations in both diffusion-dominated andconvection/reaction-dominated regimes. We present an explicit hybrid estimator,which, in each regime, is proved to be reliable and efficient with constantsindependent of the parameters in the underlying problem. Forconvection-dominated problems, the norm introduced by Verf{\"u}rth\cite{verf2005confusion} is used to measure the approximation error. Variousnumerical experiments are performed to (1) demonstrate the robustness of thehybrid estimator; (2) show that the hybrid estimator is more accurate than theexplicit residual estimator and is less sensitive to the size of reaction, eventhough both of them are robust.

Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations