  In the paper, we propose a collocation method based on multivariate
polynomial splines over triangulation or tetrahedralization for solving Stokes
and Navier-Stokes equations. We start with a detailed explanation of the method
for the Stokes equation and then extend the study to the Navier-Stokes
equations. We shall show that the numerical solution can approximate the exact
PDE solution very well over several domains. Then we present several numerical
experimental results to demonstrate the performance of the method over the 2D
and 3D settings. Also, we apply the IPBM method to our method to find the
solution over several curved domains effectively. In addition, we present a
comparison with the existing multivariate spline methods in \cite{AL02} and
several existing methods to show that the new method produces a similar and
sometimes more accurate approximation in a more efficient fashion.
