a posteriori error estimates; complementarity; index of effectivity; elliptic problem; reaction-diffusion; singular perturbation
In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky  and the reconstruction of Braess and Schöberl . We evaluate the efficiency of these flux reconstructions by their comparison with the optimal flux reconstruction computed as a global minimization problem.