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.

a b s t r a c tIn this paper an adaptive multilevel mesh refinement method, coupled with the Zienkiewicz and Zhu a posteriori error estimator, is applied to solid mechanics with the objective of conduct reliable nonlinear studies in acceptable computational times and memory space. Our automatic approach is first verified on linear behaviour, on 2D and 3D simulations. Then a nonlinear material behaviour is studied. Advantages and limitations of the local defect correction method in solid mechanics problems in terms of refinement ratio, error level, CPU time and memory space are discussed. This kind of resolution is also compared to a global h-adaptive resolution.

In this paper an adaptive multilevel mesh refinement method, coupled with the Zienkiewicz and Zhu a posteriori error estimator, is applied to solids mechanics with the objective of conducting reliable nonlinear studies in acceptable computational times and memory space. The approach presented in this paper is first validated on linear behaviour, on two and three dimensional simulations. Then nonlinear behaviour is studied. Advantages and limitations of the local defect correction method in solids mechanics problems in terms of error level, CPU time and memory space are discussed. This kind of resolution is also compared with the classical finite element resolution.