报告题目：Superconvergence of MAC Scheme for Stokes and Navier-Stokes Equations on non-uniform grids
主讲人：芮洪兴
时 间：2019.3.28（周四）下午3:30
地 点：机电楼C310
报告摘要：
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.
主讲人简介：
芮洪兴，山东大学数学学院教授，博士生导师。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。主要从事计算数学和应研究。涉及偏微分方程数值解法，科学与工程计算，渗流力学，油水资源数值模拟方法及应用软件。在有限元方法，混合元方法，有限体积元，特征线算法，区域分裂及并行算法，以及油水资源数值模拟方法研究方面发表论文150余篇，其中 SCI100余篇。
数学与统计学院
2019.3.25
