Speaker: Dr. Xiao Li （李晓博士）
Time: 11:00-12:00, 19 June 2023 (Monday) (Beijing time)
Venue: A103,Lijiao Building
Tencent Meeting ID: 138-737-952
Abstract
In this talk, I will present some recent studies on second-order stabilized linear semi-implicit numerical schemes for the nonlocal Cahn-Hilliard equation, a variant of the classic Cahn-Hilliard equation with a Laplacian replaced by a nonlocal diffusion operator. By applying the explicit extrapolation to the nonlinear term and adding appropriate stabilization terms, the resulting constant-coefficient linear schemes bring great numerical convenience, while the theoretical analysis becomes very challenging due to the lack of high-order diffusion. Resorting to the higher-order consistency estimate for the numerical schemes, we conduct the complete convergence analysis, containing the rough and refined error estimates, and justify the discrete L-infinity bound of the numerical solution as a byproduct. Moreover, the energy stability is also obtained with respect to a modified energy. Numerical experiments are conducted for a typical case involving Gaussian kernels, including the comparison between the nonlocal and local phase transitions and the long-time simulations of the coarsening dynamics.
About Dr. Li
Dr. Xiao Li is a research assistant professor in Department of Applied Mathematics at the Hong Kong Polytechnic University. He obtained his Ph.D. degree in 2016 from Beijing Normal University under the supervision of Prof. Hui Zhang. Then, he worked as a postdoctoral fellow at Beijing Computational Science Research Center with Profs. Qiang Du and Zhonghua Qiao and at University of South Carolina with Prof. Lili Ju. Since 2019, he joined the Hong Kong Polytechnic University. Dr. Li's research interest involves numerical solutions of partial differential equations, especially the efficient and stable numerical methods for phase-field equations and related problems. Dr. Li has published more than 20 papers in some international journals, such as SIAM Journal on Numerical Analysis, Mathematics of Computation, Journal of Computational Physics, and so on.
