Energy methods in 3D spline approximations of the Navier-Stokes equations

In this work,we use splines of arbitrary degree and arbitrary smoothness to .nd approximations of the 3D Navier-Stokes equations in velocity-pressure formulation. We start by showing how to use splines to solve the 3D Poisson equation,the 3D biharmonic equation and the 3D Stokes equations.For these problems the equations are put in variational form and the associated energy functional minimized over a subset of a space of splines.For the Navier-Stokes equations,we also derived based on energy arguments the discrete equations satis .ed by the solution.Numerous numerical results are provided.