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.