P-Version least squares finite element formulation for axisymmetric incompressible Newtonian fluid flow

Abstract

This paper presents a p-version least squares finite element formulation for axisymmetric incompressible Newtonian fluid flow. The partial differential equations describing the fluid motion are cast into a set of first order coupled partial differential equations involving viscous stresses as auxiliary variables. The pressure, velocities (primary variables) and the viscous stresses (auxiliary variables) are interpolated over an element using equal order, C 0, p-version hierarchical approximation functions. The p-version least squares finite element formulation is constructed using the set of first order coupled partial differential equations which results in finding a solution vector {δ} for which the partial derivatives of the error functional (integrated sum of squares of the errors resulting from individual equations for the entire discretization) with respect to the nodal degrees of freedom {δ} become zero. This is accomplished by using Newton's method with a line search. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.