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Error analysis of a high-order numerical method on fitted meshes for a time-fractional diffusion problem
2019-01-08 15:54  

报告题目:Error analysis of a high-order numerical mechod on fitted meshes for a time-fractional diffusion

          problem

报 告 人:陈虎博士

报告时间:2019年1月9日 15:30-16:30

报告地点:数统院307学术报告厅

报告摘要:In recent years, fractional derivatives are used widely for modelling physical processes. Time-

          fractional diffusion equations are used to model abnormal diffusion phenomena, where the mean square

          displacement is proportional to tα with 0<α<1. There is much current interest in the construction

          and analysis of numerical methods for the solution of such problems, which typically exhibit a weak

          singularity at the initial time t=0. In[1] a high-order scheme for Caputo fractional derivatives of

          order α∈(0,1) is proposed and analysed for time-fractional initial-value problems (IVPs) and

          initial-boundary value problems (IBVPs), on temporal meshes that are fitted to the initial weak

          singularity. In the IBVP the spatial domain is the unit square, where a spectral method is used, but

          other domains (in Rd for d≥1) and other spatial discretisations (finite element, finite difference)

          could be handled by modifying our analysis. It is proved in [1] that, when the fitted temporal mesh

          is chosen suitably, the scheme attains order 3-α convergence in the discrete L∞ norm for the 1-

          dimensional IVP, and second-order convergence in L∞(L2) for the IBVP. Numerical results demonstrate

          the sharpness of these theoretical convergence estimates.

报告人简介:陈虎,北京计算科学研究中心博士后,师从外国千人计划Martin Stynes教授,2017年北京航空航天大学获得博士

            学位。在《J. Comput. Phys.》《J. Sci. Comput.》《J. Comput. Appl. Math.》《Comput. Math. Appl.》等

            国际期刊上以第一作者身份发表SCI论文7篇。已获得博士后科学基金资助1项,国家自然科学基金青年项目1项。

            研究方向为偏微分方程数值解、谱方法以及分数阶微分方程数值方法的理论分析。

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