 
Summary: MATHEMATICS OF COMPUTATION
Volume 74, Number 250, Pages 585601
S 00255718(04)017156
Article electronically published on September 2, 2004
TRIVARIATE SPLINE APPROXIMATIONS
OF 3D NAVIERSTOKES EQUATIONS
GERARD AWANOU AND MINGJUN LAI
Abstract. We present numerical approximations of the 3D steady state Nav
ierStokes equations in velocitypressure formulation using trivariate splines
of arbitrary degree d and arbitrary smoothness r with r < d. Using func
tional arguments, we derive the discrete NavierStokes equations in terms of B
coefficients of trivariate splines over a tetrahedral partition of any given polyg
onal domain. Smoothness conditions, boundary conditions and the divergence
free condition are enforced through Lagrange multipliers. The pressure is com
puted by solving a Poisson equation with Neumann boundary conditions. We
have implemented this approach in MATLAB and present numerical evidence
of the convergence rate as well as experiments on the lid driven cavity flow
problem.
1. Introduction
There are many computational methods available in the literature for the numer
