A MULTILEVEL MESH INDEPENDENCE PRINCIPLE FOR THE NAVIER-STOKES EQUATIONS

Multilevel, finite element discretization methods for the Navier-Stoke s equations are considered. In contrast to usual multilevel methods, a superlinear scaling of the consecutive meshwidths h(j+1) = O(h(j)(alp ha(j))) is used. On the coarsest mesh the discretized system is solved , which is small and nonlinear. On each subsequent mesh only one or tw o Newton correction steps are performed, so that only one or two large r, linear systems are solved. The scalings of the meshwidths that lead to optimal accuracy of the approximate solution in both the H-1- and L(2)-norm are investigated. An error analysis of independent interest is also presented for the basic finite element method using the conser vation form of the nonlinear term. This formulation leads to a nonline ar system whose nonlinearity is easier to resolve than the systems ari sing when either the convective or explicitly skew-symmetric forms are used for the nonlinear term.