Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems

•A local multi-grid refinement method is applied to mechanical industrial test cases.•Accuracy and relevancy of two prolongations operators are discussed.•The optimal mesh convergence order with respect to the finest mesh step is obtained.•A sensibility study of the coupling with ana posteriorierror estimator (ZZ) is made.•Performances of the method are appreciated in comparison with a h-refinement strategy.

The aim of this study was to assess the efficiency of the local defect correction multi-grid method (Hackbusch, 1984 [31]) on solid mechanics test cases showing local singularities and derived from an industrial context. The levels of local refinement are automatically obtained recursively, using Zienkiewicz and Zhu’s a posteriori error estimator. Choices of the prolongation operator, the refinement ratio and criterion are discussed in order to give the most satisfactory performances. Comparisons with an h-adaptive refinement method show the efficiency of the tool presented here, in terms of its accuracy and the memory space and processor time required.