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The extended/generalized finite element method: an overview of the method and its applications. (English) Zbl 1202.74169
Summary: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems.

74S05Finite element methods in solid mechanics
74-02Research monographs (mechanics of deformable solids)
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