A finite element approach derived from the simplified variational principle

In previous papers [ we have described how by mini mizing the fluid action numerically one can obtain a solution of the fluid steady state equations. The action which was used was the four function action of Seliger& Whitham [5] In a recent paper [6] we describe how one can improve upon previous art by reducing the number of variables in the action. Three independent functions variational formalism for stationary and non-stationary barotropic flows is introduced. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field v→ and the density p. In this paper we will discuss a possible finite element approach related to the usage of the new action principles as basis for a CFD algorithms.