题目：Energy stable local discontinuous Galerkin methods for Keller-Segel chemotaxis model and nonlinear Schroedinger equation with wave operator

 报告人: 郭莉  中山大学

 

 时间： 2017年6月1日  下午 3:00-4:00 

 地点： 管理科研楼1218

报告摘要： 

In this talk, we apply local discontinuous Galerkin (LDG) methods to solve the Keller-Segel (KS) chemotaxis model and the nonlinear Schroedinger equation with wave operator (NLSW). The KS chemotaxis model may exhibit blow-up patterns with certain initial conditions, and is not easy to approximate numerically. A free energy which is decreasing during time evolution has been constructed. Even though the energy can be negative, it is always positive if the blow-up will occur. Meanwhile, the NLSW problem also has a conservative energy which is important to simulate long time behavior and eliminate oscillations. In this talk, we will construct a special energy stable LDG method to approximate the KS chemotaxis model with blow-up solution and numerically preserve the energy as well as a fully discrete energy conserving scheme utilizing the LDG method in space and the Crank-Nicholson algorithm in time to simulate the NLSW problem. Some numerical experiments for these two problems will be given to demonstrate the validity and performance of the energy stable LDG method.