Conforming finite elements based on complete polynomials

The conditions for achieving progressive improvement of finite element approximations with respect to increasing orders of (complete) polynomial approximating functions are examined. It is concluded that in certain important cases nodal variables cannot be employed in conjunction with this process. An alternative formulation of the finite element problem is discussed. In this formulation all matrices necessary for defining the numerical problem can be generated automatically; it is not necessary to refine the finite element when greater accuracy is sought, and continuity of all derivatives, including those not explicitly stated in formulating the problem, can be realized to an arbitrary degree of precision.