报告题目 (Title)：The direct discontinuous Galerkin method for a time-fractional initial-boundary value problem (时间分数阶初值问题的直接间断Galerkin方法)
报告人 (Speaker)： 黄朝宝 副教授（山东财经大学）
报告时间 (Time)：2022年10月13日(周四) 8:30-10:00
报告地点 (Place)：线上腾讯会议（会议 ID：378 158 995）
邀请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
报告摘要：In this talk, a fully discrete numerical method for the time-fractional reaction-diffusion initial-boundary value problem with a weak singularity solution is investigated, where we use the well-known L1 discretization on a graded mesh in time and a direct discontinuous Galerkin (DDG) finite element method on a uniform mesh in space. For the linear case with the periodic boundary condition, we prove that at each time level of the mesh, our L1-DDG solution is superconvergent of order k+2 in L^2 (Ω) to a particular projection of the exact solution. Moreover, the L1-DDG solution achieves superconvergence of order (k+2) in a discrete L^2 (Ω) norm computed at the Lobatto points, and order (k+1) superconvergence in a discreteH^1 (Ω) seminorm at the Gauss points. For the nonlinear case with Dirichlet boundary conditions, we derive the unconditionally optimal L^2 (Ω) norm convergent result by using the time-space splitting technical. Finally, numerical results show that our analysis is sharp.
