理学论坛第一百零四次学术活动通知(张强,杨杨报告)
发布时间: 2017-05-11   浏览次数: 146

报告1
报告题目:Some optimal error estimates of local discontinuous Galerkin method when solving convection diffusion equations
报告人张强 
报告人单位:南京大学数学系
时间:2017年5月16日14:00-15:00
地点:教2-314室
主办单位:理学院
报告内容:In this talk we present some results about the local discontinuous Galerkin (LDG) methods when solving the time-dependent convection diffusion equations. We focus on the optimal L2-norm error estimates when the generalized upwind numerical flux and generalized alternating numerical fluxes are used together, where the generalized Gauss-Radau (GGR) projection plays the important role. More difficult than the case in the global estimate, we have to establish a more deep investigation on the GGR projection and understand its global essence, in order to obtain the double-optimal local L2-norm error estimate of LDG method when solving the singularity perturbation problem. Different time-marching techniques are considered also, such as the explicit Runge-Kutta algorithm and explicit-implicit Runge-Kutta algorithm.
报告人简介:张强,南京大学数学系教授,1999年取得南开大学数学博士学位,1999年至2008年在南开大学数学系历任讲师、副教授,2008年至今在南京大学数学系任教授。张强教授的研究领域为发展型偏微分方程的稳定化有限元方法研究,包括双曲守恒律、对流占优问题、退化抛物问题等的全离散DG和LDG方法的稳定性和误差分析。张强教授在DG方法的全离散分析和局部分析方面等方面做出了一系列开创性的工作,在SIAM Journal on Numerical Analysis,Numerische Mathematik,Mathematica Computation,Journal of Scientific Computing等著名杂志发表文章30余篇。

报告2
报告题目:Local discontinuous Galerkin methods for KS chemotaxis model
报告人杨扬 
报告人单位:Department of Mathematical Sciences,Michigan Technological University(密歇根理工大学数学系)
时间:2017年5月16日15:00-16:00
地点:教2-314室主办单位:理学院
报告内容:In this talk, we will focus on local discontinuous Galerkin methods for Keller-Segel chemotaxis model, which might yield blow-up solutions. We first give the error estimates based on two different finite element spaces, and then proceed to the positivity-preserving technique to obtain positive numerical approximations. Subsequently, we will numerically demonstrate how to find the blow-up time. Finally, for the blow-up solution we can construct a special numerical energy to stabilize the scheme.
报告人简介:杨扬,2009年本科毕业于中国科学技术大学数学系,2013年博士毕业于美国布朗大学应用数学系,导师是舒其望教授,自2013年至今,在密歇根理工大学担任助理教授。杨扬博士在间断Galerkin方法的数值模拟和理论分析方面做出了很多出色的工作,比如超收敛分析、爆破解的DG方法研究、采油数值模拟等,在SIAM Journal on Numerical Analysis,Numerische Mathematik,Journal of Computational Physics,Journal of Scientific Computing等著名杂志发表文章20余篇。