Optimum Mixed Finite Element Nonlinear Galerkin Method for the Navier-Stokes211 Equations III: Convergence Analysis for Time Discretization

摘要

In this article, the authors provide a convergence analysis for the Eurler211u001eexplicit difference schemes of time discretization applied to spatial discrete 211u001eoptimum nonlinear Galerkin approximations using mixed finite elements for the two-211u001edimensional Navier-Stokes equations. The authors results show that this explicit 211u001escheme is of the convergence rate of same order as the explicit scheme related to 211u001espatial discrete Galerkin approximation under a less restrictive time step 211u001econtraint than that of the explicit scheme corresponding to spatial discrete 211u001eGalerkin approximation.