报告题目 (Title)：hp-version continuous Petrov-Galerkin time-stepping method for fourth-order parabolic equations
报告人 (Speaker)： 易利军 教授（上海师范大学）
报告时间 (Time)：2025年10月28日(周二) 15:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：李常品、蔡敏
报告摘要：In this talk, we shall introduce a fully discrete numerical scheme for fourth-order parabolic equations, which combines an hp-version continuous Petrov-Galerkin time-stepping method for temporal discretization with an hp-version C1 conforming finite element method for spatial discretization. Several a priori error estimates are established, expressed explicitly in terms of local temporal and spatial mesh sizes, local approximation degrees, and the local regularity of the exact solution. In the presence of initial singularities at t=0, we demonstrate that optimal algebraic convergence rates in time can be recovered by employing a graded temporal mesh. Moreover, we show that combining geometrically refined time partitions with a linear increase in approximation degrees yields exponential convergence in time. Numerical experiments are provided to support the theoretical results.