Local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes
报告题目(Title)：Local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes
报告人(Speaker)：Yang Yang （密歇根理工大学）
地点(Place)：后主楼1124
时间(Time)：5月24日下午4:00-5:00
邀请人(Inviter)：曹外香
报告摘要
Local discontinuous Galerkin (LDG) methods are popular for convection-diffusion equations. In LDG methods, we introduce an auxiliary variable p to represent the derivative of the primary variable u, and solve them on the same mesh. In this talk, we will introduce a new LDG method, and solve u and p on different meshes. The stability and error estimates will be investigated. The new algorithm is more flexible and flux-free for pure diffusion equations without introducing additional computational cost compared with the original LDG methods, since it is not necessary to solve each equation twice. Moreover, it is possible to construct third-order maximum-principle-preserving schemes based on the new algorithm. However, one cannot anticipate optimal accuracy in some special cases. In this talk, we will find out the reason for accuracy degeneration which further leads to several alternatives to obtain optimal convergence rates. Finally, several numerical experiments will be given to demonstrate the stability and optimal accuracy of the new algorithm.
