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数学学院、所2020年系列学术活动(第277场):李步扬 教授 香港理工大学

发表于: 2020-11-18   点击: 

报告题目:Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations

报 告 人:李步扬 教授 香港理工大学

报告时间:2020 年11 月19日上午 08:40-09:20

报告地点:腾讯会议 ID:892 255 965

会议密码:1119

校内联系人:吕俊良        lvjl@jlu.edu.cn


报告摘要: 

     A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen-Cahn equation. The proposed method consists of a kth-order multistep exponential integrator in time, and a lumped mass finite element method in space with piecewise rth-order polynomials and Gauss-Lobatto quadrature. At every time level, the extra values violating the maximum principle are eliminated at the finite element nodal points by a cut-off operation. The remaining values at the nodal points satisfy the maximum principle and are proved to be convergent with an error bound of O(τk + hr). The accuracy can be made arbitrarily high-order by choosing large k and r. Extensive numerical results are provided to illustrate the accuracy of the proposed method and the effectiveness in capturing the pattern of phase-field problems.


报告人简介:

      李步扬博士,2012 年在香港城市大学获得博士学位,2012 年起至 2016 年在南京大学作助理研究员、副教授,2015 至 2016 年在德国图宾根大学作洪堡学者。自 2016 年起李步扬博士在香港理工大学担任助理教授、副教授。李步扬博士的研究方向主要是偏微分方程的数值方法,包括非线性抛物方程、超导方程、相场方程、曲面演化方程、不可压流体方程等, 至今已发表论文70篇。