Research at FAST

92 Department of Applied Mathematics Department of Applied Mathematics Qualification BSc (BIT) PhD (BNU) Postdoc (CSRC; USC; PolyU) ORCID ID 0000-0003-3598-9077 Dr LI Xiao Research Assistant Professor Research Overview My research interests are in the area of numerical partial differential equations, with topics including finite difference method, spectral method, high-order accurate methods, energy stable schemes, maximum bound principle preserving schemes, numerical solutions of phase field equations, numerical analysis for nonlocal models, and computational fluid dynamics. Representative Publications • Qiang Du, Lili Ju, Xiao Li , and Zhonghua Qiao. Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes, SIAM Review, in press • Xiao Li , Lili Ju, and Thi-Thao-Phuong Hoang. Overlapping domain decomposition based exponential time differencing methods for semilinear parabolic equations, BIT Numerical Mathematics, in press • Xiao Li , Zhonghua Qiao, and Cheng Wang. Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, Mathematics of Computation, 90 ( 2021 ), 171-188 • Huadong Gao, Lili Ju, Xiao Li , and Ravindra Duddu. A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion, Journal of Computational Physics, 406 ( 2020 ), 109191 • Xiao Li , Lili Ju, and Xucheng Meng. Convergence analysis of exponential time differencing schemes for the Cahn-Hilliard equation, Communications in Computational Physics, 26 ( 2019 ), 1510-1529 • Qiang Du, Lili Ju, Xiao Li , and Zhonghua Qiao. Maximum principle preserving exponential time differencing schemes for nonlocal Allen-Cahn equations, SIAM Journal on Numerical Analysis, 57 ( 2019 ), 875-898 • Qiang Du, Lili Ju, Xiao Li , and Zhonghua Qiao. Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation, Journal of Computational Physics, 363 ( 2018 ), 39-54 • Lili Ju, Xiao Li , Zhonghua Qiao, and Hui Zhang. Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection, Mathematics of Computation, 87 ( 2018 ), 1859-1885 • Xiao Li , Zhonghua Qiao, and Hui Zhang. Convergence of a fast explicit operator splitting method for the epitaxial growth model with slope selection, SIAM Journal on Numerical Analysis, 55 ( 2017 ), 265-285