A two-level Schwarz method for a finite element approximation of a nonlinear biharmonic equation

摘要

In this paper, we consider a finite element approximation of a nonlinear biharmonic equation which is related to the well-known two-dimensional Navier–Stokes equations. First, optimal energy and H1-norm estimates are obtained. Second, a two-level additive Schwarz method is presented for the discrete nonlinear algebraic system. It is shown that if the Reynolds number is sufficiently small, the two-level Schwarz method is optimal, i.e., the convergence rate of the Schwarz method is independent of the mesh size and the number of subdomains.