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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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