報告題目：Superconvergence of MAC Scheme for Stokes and Navier-Stokes Equations on non-uniform grids
The marker and cell (MAC) method, a finite volume or finite difference method based on staggered grids, has been one of the simplest and most effective numerical schemes for solving the Stokes and Navier-Stokes equations. The superconvergence on uniform grids for Stokes equations has been observed since 1992 but numerical analysis was not obtained completely.
In this talk we will present the second order superconvergence in L2 norm for both velocity and pressure for the MAC scheme for Stokes and Navier-Stokes equations. We also obtain the second order superconvergence for some terms of H1 norm of the velocity, and the other terms of H1 norm are second order superconvergence on uniform grids. Numerical experiments using the MAC scheme show agreement of the numerical results with theoretical analysis. Some corresponding and extended results such as MAC finite difference based on staggered grids for Darch-Forchheimer and Stokes-Darcy problems are also mentioned.