International audienceThis paper introduces a local multilevel mesh refinement strat-egy that automatically stops relating to a user-defined tolerance even incase of local singular solutions. Refinement levels are automatically gener-ated thanks to a criterion based on the direct comparison of the a posteriorierror estimate with the prescribed error. Singular solutions locally increase with the mesh step (e.g. load discontinuities, point load or geometric in-duced singularities) and are hence characterized by locally large element-wise error whatever the mesh refinement. Then, the refinement criterionmay not be self-sufficient to stop the refinement process. Additional stop-ping criteria are required to avoid an infinite refinement process while stillrespecting the desired threshold. Two original geometry-based stopping cri-teria are proposed that consist in determining the critical region for whichthe mesh refinement becomes inefficient. Numerical examples show the effi-ciency of the methodology for stress tensor approximation in L 2 -relative orL et8734; -absolute norms
