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New Analysis of Galerkin FEMs for Nonlinear Parabolic PDEs--Unconditional Convergence

Wednesday, June 17th, 2020, 3:00 PM  Zoom 会议 ID:631 060 3119
报告人: 孙伟伟教授 北师大浸会国际学院(UIC)
Zoom 会议 ID:631 060 3119(密码:123456)

摘要: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.

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。
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