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数学学院、所2019年系列学术活动(第214场):孟祥云 北京交通大学

发表于: 2019-12-16 08:55  点击:

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:20191213 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,本科毕业于吉林大学计算数学专业,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。