Report title: Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations

Reporter: Professor Li Buyang The Hong Kong Polytechnic University

Reporting time: 08:40-09:20 AM, November 19, 2020

Report location: Tencent Conference ID: 892 255 965

Conference password: 1119

School contact: Lu Junliang lvjl@jlu.edu.cn

Report summary:

    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.

Brief introduction of the speaker:

     Dr. Li Buyang received his doctorate from the City University of Hong Kong in 2012, worked as an assistant researcher and associate professor at Nanjing University from 2012 to 2016, and worked as a Humboldt Scholar at the University of Tubingen in Germany from 2015 to 2016. Since 2016, Dr. Li Buyang has been an assistant professor and associate professor at the Hong Kong Polytechnic University. Dr. Li Buyang's research direction is mainly on the numerical methods of partial differential equations, including nonlinear parabolic equations, superconducting equations, phase field equations, surface evolution equations, incompressible fluid equations, etc. He has published 70 papers so far.