LAUSR

Abstract A simple flux reconstruction for finite element solutions of reaction–diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction–diffusion problem. The flux reconstruction is based on simple, independent post-processing operations over patches of elements in conjunction with standard Raviart–Thomas vector fields. We prove that the corresponding local error indicators are locally efficient and robust (up to a nonstandard oscillation term) with respect to any mesh size and any size of the reaction coefficient, including the singularly perturbed limit.