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A simple flux reconstruction for finite element solutions ofreaction-diffusion problems is shown to yield fully computable upper bounds onthe energy norm of error in an approximation of singularly perturbedreaction-diffusion problem. The flux reconstruction is based on simple,independent post-processing operations over patches of elements in conjunctionwith standard Raviart--Thomas vector fields and gives upper bounds even incases where Galerkin orthogonality might be violated. If Galerkin orthogonalityholds, we prove that the corresponding local error indicators are locallyefficient and robust with respect to any mesh size and any size of the reactioncoefficient, including the singularly perturbed limit.

A Simple Approach to Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Problems