报告题目：A unified superconvergent postprocessing technique for Galerkin time-stepping methods

报 告 人：易利军，上海师范大学

报告摘要：We propose a unified postprocessing technique for Galerkin methods (including CG and DG) applied to solve initial value problems for first and second-order ODEs. The core idea of this postprocessing technique is to augment the existing Galerkin approximation of degree $k$ with an additional term involving a generalized Jacobi polynomial (multiplied by appropriate coefficients) of degree $k+1$. The theoretical findings suggest that, through postprocessing, the convergence rate of the original Galerkin approximation error can be elevated by one order. As an application, we extend this postprocessing technique to the Galerkin time discretization of nonlinear parabolic and hyperbolic equations in the temporal direction. Abundant numerical results underscore the effectiveness and high accuracy of the proposed postprocessing technique.

报告人简介：易利军，上海师范大学数学系教授，博士生导师。主要从事积分和微分方程的高精度数值方法（尤其是谱方法和hp有限元方法）的理论及其应用研究。主持多项国家自然科学基金（2项面上）、教育部博士点基金、上海市自然科学基金和上海市优秀青年教师资助计划等项目；获2023年度上海市自然科学奖二等奖；在《SIAM J. Numer. Anal.》、《Math. Comp.》、《Math. Models Methods Appl. Sci.》、《IMA J. Numer. Anal.》和《中国科学：数学》等国内外期刊发表论文50余篇。

报告时间：2024年12月7日 15:30-16:30

报告地点：文渊楼B536

主办单位：数学与统计学院