A Finite Element Approach Derived From the Simplified Variational Principle

In previous papers [1–4] we have described how by minimizing 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 ν⃗ and the density ρ. 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.