Construction of shape functions for the h- and p-versions of the FEM using tensorial product

This paper presents an uniform and unified approach to construct h- and p-shape functions for quadrilaterals, triangles, hexahedral and tetrahedral based on the tensorial product of one-dimensional Lagrange and Jacobi polynomials. The approach uses indices to denote the one-dimensional polynomials in each tensorization direction. The appropriate manipulation of the indices allows to obtain hierarchical or nonhierarchical and inter-element C0 continuous or non-continuous bases. For the one-dimensional elements, quadrilaterals, triangles and hexahedral, the optimal weights of the Jacobi polynomials are determined, the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated. A brief discussion of the use of sum factorization and computational implementation is considered. Copyright q 2006 John Wiley & Sons, Ltd