This paper presents an overview of an efficient FEM solver with an accuracy control strategy using automatic local grid refinement. Cheap accuracy estimators are briefly described and some concepts concerning a multigrid FE solver are presented. Several (2D / 3D) numerical examples demonstrate the efficiency of the proposed strategy in terms of computation time and memory requirement. Some large scale calculations are presented, up to 200 million degrees of freedom. A particular implementation care has been devoted to ensure both a linear time complexity of every intermediate step and a minimal memory requirement.