报告题目：Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes
using barrier functions

报 告 人：孟祥云 北京交通大学

报告时间：2019年12月13日 9:00-10:00

报告地点：数学楼625

报告摘要：

An initial-boundary value problem with a Caputo time derivative of fractional order between 0 and 1 is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple and general numerical-stability analysis using barrier functions, which yields sharp pointwise-in-time error bounds on quasi-graded temporal meshes with arbitrary degree of grading. L1-type and Alikhanov-type discretization in time are considered. In particular, those results imply that milder (compared to the optimal) grading yields optimal convergence rates in positive time. Semi-discretizations in time and full discretizations are addressed. The theoretical findings are illustrated by numerical experiments.

报告人简介：

孟祥云，北京交通大学教师，本科毕业于yl23411永利官网登录计算数学专业，博士毕业于北京大学数学科学学院。主要从事奇异摄动问题、分数阶方程等问题的研究。