A NOTE ON CONSTANT-FREE A POSTERIORI ERROR ESTIMATES

摘要

In this note we look at constant-free a posteriori error estimates from a different perspective. We show that they can be interpreted as an alternative way of expressing the residual of a finite element approximation and thus fit into the same framework as other a posteriori error estimates such as residual error indicators. Our approach also reveals that, when applied to singularly perturbed reaction-diffusion or convection-diffusion problems, constant-free a posteriori error estimates will not be fully robust unless extra measures are taken.