Higher order stable generalized finite element method

The generalized finite element method (GFEM) is a Galerkin method, where the trial space is obtained by augmenting the trial space of the standard finite element method (FEM) by non-polynomial functions, called enrichments, that mimic the local behavior of the unknown solution of the underlying variational problem. The GFEM has excellent approximation properties, but its conditioning could be much worse than that of the FEM. However, if the enrichments satisfy certain properties, then the conditioning of the GFEM is not worse than that of the standard FEM, and the GFEM is referred to as the stable GFEM (SGFEM). In this paper, we address the higher order SGFEM that yields higher order convergence and suggest a specific modification of the enrichment function that guarantees the required conditioning, yielding a robust implementation of the higher order SGFEM.