Abstract The strain softening behavior due to the development of damage is well known to produce unrealistic mesh sensitivity in standard finite element applications. In the present paper, a nonlocal continuum damage model is used to regularize the problem. The accuracy of the nonlocal finite element results is assessed introducing a nonlocal error estimator based on the “mechanical error” concept brought about by Ladevèze. To account for the dissipative nature of the problem, a time-step incremental error estimator is also proposed and comparatively tested. It is shown how the obtained information about the error distribution can be used for the accuracy assessment of different meshes. It is also shown how mesh refinement in the late stage of damage growth could be effectively driven by the estimate of the process zone width, based on the analytical derivation of the localization width.