Chahine, E.; Laborde, P.; Renard, Y. A reduced basis enrichment for the eXtended finite element method. (English) Zbl 1160.74407 Math. Model. Nat. Phenom. 4, No. 1, 88-105 (2009). 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. Cited in 6 Documents 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 Keywords:fracture; finite element method; Xfem; reduced basis; error estimates Software:XFEM PDFBibTeX XMLCite \textit{E. Chahine} et al., Math. Model. Nat. Phenom. 4, No. 1, 88--105 (2009; Zbl 1160.74407) Full Text: DOI EuDML Link