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A Reduced Basis Enrichment for the eXtended Finite Element Method

E. ChahineP. LabordeY. Renard — 2009

Mathematical Modelling of Natural Phenomena

This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal error estimate and some computational tests including a comparison with some other strategies.

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