报告题目：High-order two-grid compact difference method for the nonlinear time-fractional biharmonic problems
报 告 人：付红斐 教授
报告摘要：In this work, we propose a basic analysis framework of the high-order two-grid difference algorithm for nonlinear partial differential equations, which are rarely studied in the literature due to, e.g. the lack of appropriate accuracy-preserving mapping operators between two discrete grids. Concerning this issue, we introduce and analyze a high-order mapping operator between two grids to support the construction of the scheme for nonlinear time-fractional biharmonic equation. The cut-off technique and the auxiliary scheme approach are used to reduce the requirement on the nonlinear term to the local Lipschitz continuous condition, and $H^2$ estimates are performed to avoid the usage of the inverse estimates and thus the time-step conditions. To treat the fractional operator, the Alikhanov's scheme on the graded mesh is applied to deal with the weak singularity at initial time $t=0$, while the compact difference method based on the order reduction is employed for high-order spatial discretization. We integrate the above methods and improvements as well as the properties of the high-order mapping operator with the analysis of two-grid method to prove the unique solvability and the unconditionally $\alpha$-robust error estimates of the proposed schemes under $L^\infty(L^2)$ and $L^\infty(H^2)$ norms. The developed techniques are further extended to discretize and analyze the two-grid method of two-dimensional problems. Numerical examples are provided to verify the effectiveness and efficiency of the two-grid algorithms.
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。目前主要从事高精度偏微分方程数值解法和分数阶微分方程数值理论和快速算法方面的研究工作。先后主持国家自然科学基金3项、山东省自然科学基金2项等。在Computer Methods in Applied Mechanics and Engineering、Journal of Computational Physics、Journal of Scientific Computing、Fractional Calculus and Applied Analysis等发表SCI论文50余篇。2016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。
报告时间：2022年11月11日9:00-11:00
报告地点：腾讯会议ID: 128 544 231
主办单位：伟德国际1946源自英国
