Keywords: mesh adaptivity, industrial context, discretization errors, h-adaptivity remeshing.

Adaptive strategies are a necessary tool to make finite element analysis applicable to engineering practice [5]. In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to attain a prescribed accuracy [6,3]. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper we propose the use of alternative mesh refinement with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria (MR) are based on: prescribed number of elements with maximum accuracy, prescribed CPU time with maximum accuracy and prescribed memory size with maximum accuracy. These adaptive strategies are based on a technique of error in constitutive relation [7] (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas [1]. The alternative mesh generation criteria have been proposed for 2D elastic problems [2] . This work proposes the extension of alternative mesh refinement criteria for 3D elastic problems by using a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D [4].

1

P. Coorevits, P. Ladevèze, J.P. Pelle, "Mesh optimization for problems with steep gradients", Eng. Comp., 11, 129-144, 1994. doi:10.1108/02644409410799245

2

P. Coorevits, E. Bellenger,"Alternative mesh optimality criteria for h-adaptive finite element method", Finite Elements in Analysis and Design, 40, 1195-1215, 2004. doi:10.1016/j.finel.2003.08.007

3

P. Díez, A. Huerta, "A unified approach to remeshing strategies for finite element h-adaptivity", Comp. Meth. in Appl. Mech. and Engng., 176, 215-229, 1999. doi:10.1016/S0045-7825(98)00338-7

4

P.L. George, "Génération automatique de maillages: Applications aux méthodes d'éléments finis", Collection Recherche en Mathématiques Appliquées, Masson, 1991.

5

A. Huerta, A. Rodríguez-Ferran, P. Díez and J. Sarrate, "Adaptive finite element strategies based on error assessment", Int. J. for Num. Meth. Eng., 46, 1803-1818, 1999. doi:10.1002/(SICI)1097-0207(19991210)46:10<1803::AID-NME725>3.3.CO;2-V

6

P. Ladevèze, D. Leguillon, "Error estimate procedure in the finite element method and applications", SIAM J. Num. Anal., 20, 485-509, 1983. doi:10.1137/0720033

7

P. Ladevèze, J.P. Pelle, P. Rougeot, "Error estimation and mesh optimization for classical Finite Elements", Eng. Comp., 8, 69-80, 1991. doi:10.1108/eb023827

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