Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem

Abstract

AbstractThis paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem. We solve a small Navier-Stokes problem on the coarse mesh with mesh size H and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size h. The error estimates derived show that if we choose h = O (|logh|1/2H3), then the two-level method we provide has the same H1 and L2 convergence orders of the velocity and the pressure as the one-level stabilized method. However, the L2 convergence order of the velocity is not consistent with that of one-level stabilized method. Finally, we give the numerical results to support the theoretical analysis.