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。
