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

翻译：我们认为,在扩散占主导地位的和对流/反应占主导地位的制度中,对对流-扩散-反应等式的事后误差估计都是有效的。我们提出了一个明确的混合估测器,在每种制度中,该测算器都证明是可靠的和高效的,而其常数与根本问题的参数无关。对于对流问题,用Verf {u}rth}{cite{verf2005convunch}提出的规范来衡量近似差。进行了各种数字实验,以便:(1) 显示混合估测器的坚固性;(2) 表明混合估测器比明确的残留估测器更准确,对反应的大小也不太敏感,尽管两者都很健全。