内容摘要：

The marker and cell (MAC) method, a finite volume method based on staggered grids, has been one of the simplest and most effective numerical schemes for solving the Stokes and Navier-Stokes equations. Its superconvergence on uniform grids has been observed since 1992 but numerical analysis was not obtained completely. In this paper we establish the LBB condition and the stability for both velocity and pressure for MAC scheme of Stokes equations on non-uniform grids. Then we construct a auxiliary function depending on the velocity and discretizing parameters and analyze the superconvengence by using this function. We obtain the second order superconvergence in L2 norm for both velocity and pressure for the MAC scheme. 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.

主讲人介绍：

山东大学教授，理学博士，博士生导师，山东大学数学学院副院长。主要从事计算数学和应用数学研究，包括有限元和混合元方法，有限体积元，差分算法，特征线算法等偏微分方程数值解法，流体及渗流力学问题数值模拟方法及应用软件。发表论文140余篇，其中 SCI收录近百余篇。现任中国工业与应用数学学会常务理事、中国计算物理学会常务理事，曾任中国计算数学学会常务理事。