The design and analysis of the generalized finite element method (Q1970179)

This paper gives an overview of the generalized finite element method (GFEM). This method extends the classical FEM by adding special functions which reflect for example singular functions obtained in the neighborhood of a corner point. After a short view on the approximability the authors attach greater importance to explain how to handle the linear dependence of the resulting stiffness matrix and they show how adaptive quadrature algorithms can be included. In several realistic examples they examine the convergence of the GFEM approximation.