题目：Error estimates of local discontinuous Galerkin method with generalized alternating uxes for convection di usion eqautions
摘要：In this talk we shall discuss the local discontinuous Galerkin methodswith the generalized upwind numerical ux and generalized alternating nu-mericaluxes, when solving one- and/or two-dimensional convection di u-sion problems. Firstly the periodic condition is considered and the globalL2-norm error estimate is optimal. To do that, we will introduce the gener-alized Gauss-Radau (GGR) projection, which is de ned globally, not locally.Secondly the singularity perturbation of convection di usion equation with
Dirichlet condition is considered, which has a stationary outow boundarylayer. The local L2-norm error estimate is double-optimal, namely, not onlythe width of pollution domain is optimal, and also the order of L2-norm errorout of pollution domain is optimal. To this purpose, we will introduce suit-able weight functions nearby the outow boundary, and carefully establish adeep investigation on the GGR projection.
报告题目：Stability and error estimates of implicit-explicit local discontinuous Galerkin methods
报告摘要：In this talk, a type of fully-discrete local discontinuous Galerkin (LDG) methods will be presented for convection-diffusion problems and incompressible fluid flow, where the implicit-explicit (IMEX) schemes are adopted in time discretization. The IMEX schemes can overcome the small time step restriction compared with explicit schemes, and they are more efficient than implicit schemes. Unconditional stability and optimal error estimates are proved for the considered IMEX-LDG schemes, and several numerical experiments are given to verify the theoretical analysis.