Convergence and stability of finite element modified method of characteristics for the incompressible Navier–Stokes equations

Abstract

We present a convergence and stability analysis of the finite element modified method of characteristics for the incompressible Navier–Stokes equations. The method consists of combining a second-order backward time discretization based on the characteristics method with a spatial discretization of finite element type. We obtain stability results and optimal error estimates in the L 2-norm for velocity and pressure components under a time step restriction more relaxed than the standard Courant–Friedrichs–Levy condition. We also show some numerical results for two benchmark problems on the incompressible Navier–Stokes equations at different Reynolds numbers.