Une méthode d’éléments finis étendue d’ordre supérieur optimale
Keywords:
fracture, finite elements, XFEM, optimal rate of convergence, pointwise matchingAbstract
We present some modifications of the classical extended finite element method to achieve the same rate of convergence in fracture mechanics than using standard finite elements for a smooth problem. The first improvement consists in enriching an enlarged area around the crack tip. We also consider a bounding condition between the degrees of freedom of enrichment. Finally, a matching condition on the boundary of the enriched area is introduced. In such a nonconformal method, any blending element partially enriched with the asymptotic crack tip displacement solutions is considered. Numerical results on a test problem confirm optimality for finite elements of higher order.
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