学术报告20260603：Barrier function local and global analysis of an L1 finite element method for a multiterm time-fractional initial-boundary value problem

报告人：孟祥云 副教授 北京交通大学

报告题目：Barrier function local and global analysis of an L1 finite element method for a multiterm time-fractional initial-boundary value problem

摘 要：A multiterm time-fractional initial-boundary value problem is considered. To solve the problem numerically, we apply the L1 discretisation to each fractional derivative on a graded temporal mesh, together with a standard finite element method for the spatial derivatives on a quasiuniform spatial mesh. A new proof of the stability of this method, which is more complicated than the case of a single fractional derivative, is given using barrier functions; this powerful new technique leads to sharp error estimates at each time level that show precisely the improvement in accuracy of the method as one moves away from the initial time. (A result of this type has not previously been derived for this multiterm problem.) Numerical experiments show the sharpness of our theoretical results.

报告人简介：孟祥云，北京交通大学数学与统计学院副教授。2016年博士毕业于北京大学数学科学学院，2016-2019年在北京计算科学研究中心做博士后工作。主要从事偏微分方程数值解、奇异摄动及分数阶等问题研究。主持国家自然科学基金青年项目1项、参与国家自然科学基金面上项目。研究成果发表在SIAM J. Numer. Anal.、J. Sci. Comput.等杂志。

报告时间：2026年6月3日，09:00--12:00

报告地点：腾讯会议（会议号：514-328-410）

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内蒙古大学数学科学学院

2026年5月29日