6月17日 孙伟伟:New Analysis of Galerkin FEMs for Nonlinear Parabolic PDEs-- Unconditional Convergence

来源:中国足球竞彩比分 时间:2020-06-09浏览:49设置


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

开始来源:中国足球竞彩比分 时间:2020-06-17   15:00:00    结束来源:中国足球竞彩比分 时间:2020-06-17   16:00:00

讲座地址:Zoom  会议   ID631 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  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.

 


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