On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on thenonexistence of pyramidal polynomial basis functions. Then wepresent a new symmetric composite pyramidal finite element whichyields a better convergence than the nonsymmetric one. It hasfourteen degrees of freedom and its basis functions are incompletepiecewise triquadratic polynomials. The space of ansatz functionscontains all quadratic functions on each of four sub-tetrahedra thatform a given pyramidal element.