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A reduced basis enrichment for the eXtended finite element method. (English) Zbl 1160.74407

Summary: 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 a priori error estimate and some computational tests including a comparison with some other strategies.

MSC:

74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Software:

XFEM
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