A NEW TRIANGULAR AND TETRAHEDRAL BASIS FOR HIGH-ORDER (HP) FINITE-ELEMENT METHODS

In this paper we describe the foundations of a new hierarchical modal basis suitable for high-order (hp) finite element discretizations on u nstructured meshes. It is based on a generalized tensor product of mix ed-weight Jacobi polynomials. The generalized tensor product property leads to a low operation count with the use of sum factorization techn iques. Variable p-order expansions in each element are readily impleme nted which is a crucial property for efficient adaptive discretization s. Numerical examples demonstrate the exponential convergence for smoo th solutions and the ability of this formulation to handle easily very complex two- and three-dmensional computational domains employing sta ndard meshes.