报告题目：A two-grid block-centered finite difference method for the nonlinear RLW equation

报告人：付红斐教授  中国海洋大学
　　报告时间： 2022年6月15日（星期三）下午16：30
　　报告地点：文理楼254

报告人简介：

付红斐，中国海洋大学数学科学学院教授、博士生导师，中国工业与应用数学学会油水资源数值方法专委会委员。主要从事偏微分方程数值解法、最优控制问题数值算法和分数阶微分方程数值理论和快速算法方面的研究和教学工作。先后主持国家自然科学基金、山东省自然科学基金等10余项。在Computer Methods in Applied Mechanics and Engineering、Journal of Computational Physics、Journal

of Scientific Computing等发表SCI论文50余篇。2015年，获山东省科学技术奖自然科学二等奖（排名第3），2020年入选中国海洋大学“青年英才工程”第一层次人才计划。

报告摘要：

In this talk, a Crank-Nicolson block-centered finite difference method is first introduced and analyzed for the nonlinear regularized long wave equation. By using a cutoff technique, second-order convergence both in time and space are proved under a suitable  time-space stepsize constraint condition. To further  improve the computational efficiency, an efficient two-grid block-centered finite difference method is  introduced and analyzed, in which a resulting small-scale nonlinear problem is first solved on a coarse grid space of size $H$, and then a resulting large-scale linear problem is solved on a fine grid space of size $h$.  Under a rough time-space stepsize constraint condition $\Delta t= o (H^{1/4})$, optimal-order error estimates for both the primal variable and its flux are derived on non-uniform spatial grids. Thus, the proposed method is competitive both in accuracy and efficiency compared with the fully nonlinear Crank-Nicolson block-centered finite difference scheme. Numerical experiments are presented to verify the theoretical analysis.