Fully tensorial nodal and modal shape functions for triangles and tetrahedra

This paper presents nodal and modal shape functions for triangle and tetrahedron finite elements. The functions are constructed based on the fully tensorial expansions of one-dimensional polynomials expressed in barycentric co-ordinates. The nodal functions obtained from the application of the tensorial procedure are the standard h-Lagrange shape functions presented in the literature. The modal shape functions use Jacobi polynomials and have a natural global C0 inter-element continuity. An efficient Gauss–Jacobi numerical integration procedure is also presented to decrease the number of points for the consistent integration of the element matrices. An example illustrates the approximation properties of the modal functions.