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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 L2-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.
Key Words: Numerical analysis,; incompressible Navier–Stokes equations,; modified method of characteristics,; finite element method
Published Online: 2007-08-13
Published in Print: 2007-07-20
Copyright 2007, Walter de Gruyter
