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Fully Discrete hp-Finite Elements: Fast Quadrature
(1999)SAM Research ReportA fully discrete hp finite element method is presented. It combines the features of the standard hp finite element method (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 .Report -
The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions
(1999)SAM Research ReportThe Streamline Diffusion Finite Element Method (SDFEM) for a two dimensional convection-diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes" which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such ...Report