Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics

Abstract. Drawing inspiration from the extended finite element method (X-FEM), we propose for two-dimensional elastic fracture problems, an virtual (X-VEM). In X-VEM, extend standard space with product of vector-valued nodal shape functions and suitable enrichment fields, which reproduce singularities exact solution. We define projection operator that maps in onto a set spanned by linear polynomials augmented fields. Several numerical examples are adopted to illustrate convergence accuracy proposed method, both quadrilateral general polygonal meshes.