Document

Buyang Li

Professor and RGC Research Fellow
Department of Applied Mathematics
The Hong Kong Polytechnic University
Hung Hom, Hong Kong
Email address: buyang.li@polyu.edu.hk
https://orcid.org/0000-0001-7566-3464

Curriculum Vitae

Research Interests     Publication     Research Group     PhD, Postdoc and Visiting Scholar Positions

  • Numerical methods and analysis for partial differential equations, including
  • Surface evolution under geometric flows, geometric evolution equations, PDEs on surfaces ← click here
    1. A new approach to the analysis of parametric finite element approximations to mean curvature flow (PDF)
    2. New artificial tangential motions for parametric finite element approximation of surface evolution (PDF)
    3. A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field (PDF)
    4. Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow (PDF)
    5. Convergence of Dziuk’s semidiscrete finite element method for mean curvature flow of closed surfaces (PDF)
    6. Convergence of Dziuk's linearly implicit parametric finite element method for curve shortening flow (PDF)
    7. A convergent evolving finite element algorithm for Willmore flow of closed surfaces (PDF)
    8. A convergent evolving finite element algorithm for mean curvature flow of closed surfaces (PDF)

    9. Convergence of finite elements on an evolving surface driven by diffusion on the surface (PDF)

    10. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems (PDF)

      Mean curvature flow:

      Willmore flow:

  • Low-regularity approximation to nonlinear dispersive equations
  • Incompressible Navier–Stokes equations
  • Semilinear parabolic equations and phase field equation
  • Interior penalty finite element methods and perfectly matched layer (PML) for the Helmholtz equation
  • Maximal Lp-regularity of time discretization methods for parabolic equations
  • Maximum-norm stability and maximal Lp-regularity of finite element methods
  • High-order approximation of singular solutions of fractional evolution equations
  • Dynamic Ginzburg–Landau superconductivity equations in nonsmooth domains
  • Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity (PDF)
  • Editorial boards

  • Mathematics of Computation:                 2022.2 –– present

  • SIAM Journal on Numerical Analysis:   2022.1 –– present

    Awards

  • RGC Research Fellow Award 2023 (by the Hong Kong Research Grants Council).

  • The Hong Kong Mathematical Society Young Scholars Award 2022.

  • Alexander von Humboldt Research Fellowship, 2015-2016.

  • Best Paper Award for Young Scholars 2013, The Chinese Society for Computational Mathematics
         (于第十二届全国高校计算数学年会).