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
Numerical methods and analysis for partial differential equations, including
- Surface evolution under geometric flows, geometric evolution equations, PDEs on surfaces
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- Fluid-structure interation and moving interface problems
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- Low-regularity approximation to nonlinear dispersive equations
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An unfiltered low-regularity integrator for the KdV equation with solutions below H1
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Numerical approximation of discontinuous solutions of the semilinear wave equation
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A new second-order low-regularity integrator for the cubic nonlinear Schrödinger equation
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A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
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A semi-implicit exponential low-regularity integrator for the Navier-Stokes equations
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A constructive low-regularity integrator for the 1d cubic nonlinear Schrödinger equation under the Neumann boundary condition
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A second-order low-regularity correction of Lie splitting for the semilinear Klein-Gordon equation
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- Incompressible Navier–Stokes equations
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- Nonlinear parabolic equations and phase field equation
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- Interior penalty finite element methods and perfectly matched layer (PML) for the Helmholtz equation
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- Maximal Lp-regularity of time discretization methods for parabolic equations
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- Maximum-norm stability and maximal Lp-regularity of finite element methods
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- High-order approximation of singular solutions of fractional evolution equations
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- Dynamic Ginzburg–Landau superconductivity equations in nonsmooth domains
- Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity
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