New shape functions for triangular p-FEM using integrated Jacobi polynomials

In this paper, the second order boundary value problem -del center dot (A(x,y) del u)=f is discretized by the Finite Element Method using piecewise polynomial functions of degree p on a triangular mesh. On the reference element, we define integrated Jacobi polynomials as interior ansatz functions. If A is a constant function on each triangle and each triangle has straight edges, we prove that the element stiffness matrix has not more than 25/2 p(2) nonzero matrix entries. An application for preconditioning is given. Numerical examples show the advantages of the proposed basis.