This paper presents a numerical study of a posteriori error estimators for convection-diffusion equations. The study involves the gradient indicator, an a posteriori error estimator which is based on gradient recovery, three residual-based error estimators for different norms, and two error estimators which are defined by solutions of local Neumann problems. They are compared with respect to the reliable estimation of the global error and with respect to the accuracy of the computed solutions on adaptively refined grids. The numerical study shows for both criteria of comparison that none of the considered error estimators works satisfactorily in all tests.
John, V. (2000). Numerical study of a posteriori error estimators for convection-diffusion equations. Computer Methods in Applied Mechanics and Engineering, 190(5–7), 757–781. https://doi.org/10.1016/S0045-7825(99)00440-5