Keynote Speaker:Li Buyang

Abstract:

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(τ^k + h^r). The accuracy can be made arbitrarily high-order by choosing large k and r. Numerical results will be provided to illustrate the accuracy of the proposed method and the effectiveness in capturing the pattern of phase-field problems.

Speaker Introduction:

Li Buyang, an associate professor at the Hong Kong Polytechnic University, obtained a bachelor's degree in Mathematics from Shandong University in 2005 and the master's degree in Applied Mathematics, master's degree in Philosophy and a doctor's degree from City University of Hong Kong in 2007, 2009 and 2012 respectively. From 2013 to 2015, he worked as an assistant researcher at Nanjing University. From 2015 to 2016, he was a Humboldt research fellow at the University of Tubingen in Germany and joined the Department of Applied Mathematics of the Hong Kong Polytechnic University in June 2016. Professor Li's research interest is mainly the Numerical solution of differential equations, including nonlinear parabolic equations, phase-field equations, geometric curved surface evolution equations. Up to now, he has published more than 40 papers in famous SCI magazines of computational mathematics such asSIAM J. Numer. Anal.,Numer. Math.,Math. Comput.,J. Comput. Phys.

Inviter:

Jiang Xiaoyun Professor of School of Mathematics

Time:

10:40-11:30on November 28 (Saturday)

Location:

Tencent Meeting, Meeting ID:782 591 290

Click the link to attend the meeting, or add to the meeting list:

https://meeting.tencent.com/s/kXABuXE4hbgt

Hosted by: School of Mathematics, Shandong University