报告人：李步扬（香港理工大学）

邀请人:  覃婷婷

报告时间：2021年8月4日（星期三）15:00-17:00

报告地点：腾讯会议 291 268 625

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

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(\tau^k+h^r). 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.