Fully discrete hp-finite elements: fast quadrature Original Research Article

A fully discrete hp-finite element method (FEM) is presented. It combines the features of the standard hp-FEM (conforming Galerkin formulation, variable order quadrature schemes, geometric meshes, static condensation) and of the spectral element method (special shape functions and spectral quadrature techniques). The speed-up (relative to standard hp elements) is analyzed in detail both theoretically and computationally.