报告问题 (Title)：The h-p version continuous Petrov-Galerkin method for Volterra integro-differential equations (Volterra积分微分方程的h-p一连Petrov-Galerkin要领)

报告人 (Speaker)：易利军 教授（上海师范大学）

报告时间 (Time)：2022年9月29日(周四) 15:30-17:00

报告所在 (Place)：线上腾讯聚会 （ID：775 118 787）

约请人(Inviter)：蔡敏

主理部分：理学院数学系

报告摘要：In this talk, we consider an h-p version of the continuous Petrov-Galerkin time-stepping method for linear and nonlinear Volterra integro-differential equations with smooth and non-smooth kernels. We establish a priori error estimates in the L^2 -, H^1- and L^\infty-norm that are completely explicit with respect to the local discretization and regularity parameters. Moreover, we show that exponential rates of convergence can be achieved for solutions with start-up singularities by using geometrically time partitions and linearly increasing polynomial degrees. Numerical experiments are provided to illustrate the theoretical results. This presentation is based on joint works with Prof. Benqi Guo (University of Manitoba).