时间分数阶初值问题的直接间断Galerkin方法

2022.10.10

投稿:龚惠英部门:理学院浏览次数:

活动信息

时间: 2022年10月13日 08:30

地点: 腾讯会议

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.

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