讲座题目：New Analysis of Galerkin FEMs for Nonlinear Parabolic PDEs-- Unconditional Convergence 主讲人：孙伟伟 教授 主持人：郑海标 副教授 开始时间💄：2020-06-17 15:00:00 结束时间🟣：2020-06-17 16:00:00 讲座地址🤼♀️⚓️：Zoom 会议 ID👎：631 060 3119 密码🏃🏻♂️：123456 主办单位🔒：数学科学学院
报告人简介🙆： 孙伟伟教授✦，西北工业大学学士，西安交通大学硕士⛹️，加拿大温莎大学博士，专业为应用数学🧎🏻♂️➡️。知名计算数学专家，曾担任香港城市大学教授🦪，2020 年 1 月加入 UIC。主要的研究方向是科学计算与数学模型👷🏿♀️，包括有高阶数值方法、数学模型💂🏼♂️、电磁场的计算等，近几年针对非线性抛物问题提出了一套新的框架性的分析方法---无条件误差估计。孙伟伟教授担任以下期刊的编委：《 International Journal of Numerical Analysis and Modeling》和《 Numerical Mathematics: Theory, Methods and Applications》，发表科研论文上百篇，其中在SIAM系列期刊上合作发表论文30余篇。
报告内容： Linearized (semi)-implicit schemes are the most commonly-used approximations in numerical solution of nonlinear parabolic equations since at each time step, the schemes only require the solution of a linear system. However the time step restriction condition of schemes is always a key issue in analysis and computation. For many nonlinear parabolic systems, error analysis of Galerkin type finite element methods with linearized semi-implicit schemes in the time direction is established usually under certain time step condition $\tau \le h^{\alpha}$ for some $\alpha>0$. Such a time-step condition may result in the use of a very small time step and extremely time-consuming in practical computations. The problem becomes more serious when a non-uniform mesh or adaptive meshing is used. In this talk, we introduce a new approach to unconditional error analysis of linearized semi-implicit Galerkin FEMs for a large class of nonlinear parabolic PDEs. Our approach may provide a new understanding on the commonly-used schemes and clear up the misgivings for the time-step size restriction in practical computations. |
