Abstract
A p-version least squares finite element formulation (LSFEF) is presented for three-dimensional Navier-Stokes equations for isothermal, incompressible Newtonian fluid flow. The Navier-Stokes equations are cast into a set of first order partial differential equations using pressure-velocity-stress form where the stresses are auxiliary variables. The pressure, velocities and stresses are interpolated using equal order p-version hierarchical approximation functions derived from the Lagrange family of interpolation function. Newton's method with line search is used to find a solution vector {δ} which satisfies necessary and sufficient conditions resulting from least squares minimization procedure. Numerical examples are presented to demonstrate convergence characteristics and accuracy of the formulation. Numerical results are compared with analytical solutions and the results reported by other researchers.
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