Buyang Li 李步揚
Department of Applied Mathematics
The Hong Kong Polytechnic University
Hung Hom, Kowloon, Hong Kong
Office:
Room TU810, Yip Kit Chuen Building
Email:
buyang.li@polyu.edu.hk
Phone:
(+852) 3400 3416
Research Interests
Publication
PhD students and Postdocs
PhD and Postdoc Positions available
X. Gui, B. Li, and J. Wang:
Convergence of renormalized finite element methods for heat flow of harmonic maps
.
SIAM J. Numer. Anal.
(2022).
B. Kovács, B. Li, and C. Lubich:
A convergent evolving finite element algo- rithm for Willmore flow of closed surfaces
.
Numer. Math.
(2021).
B. Li and Y. Wu:
A fully discrete low-regularity integrator for the 1d periodic cubic nonlinear Schrödinger equation
.
Numer. Math.
149 (2021), pp. 151–183.
B. Li:
A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier–Stokes equations
.
Numer. Math.
147 (2021), pp. 283–304.
B. Li:
Maximal regularity of multistep fully discrete finite element methods for parabolic equations
.
IMA J. Numer. Anal.
(2021), DOI: 10.1093/imanum/drab019
B. Li:
Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements
.
SIAM J. Numer. Anal.
59 (2021), pp. 1592–1617.
X. Feng, B. Li, S. Ma:
High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation
.
SIAM J. Numer. Anal.
59 (2021), pp. 1566–1591.
G. Akrivis, B. Li, and J. Wang:
Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation
.
SIAM J. Numer. Anal.
59 (2021), pp. 265–288.
D. Leykekhman and B. Li:
Weak discrete maximum principle of finite element methods in convex polyhedra
.
Math. Comp.
90 (2021), pp. 1–18.
W. Jiang and B. Li:
A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves
.
J. Comput. Phys.
443 (2021), article 110531.
B. Li, H. Wang, and J. Wang:
Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
.
ESAIM: Math. Model. Numer. Anal.
55 (2021), pp. 171–207.
W. Cai, B. Li, and Y. Li:
Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions
.
ESAIM: Math. Model. Numer. Anal.
55 (2021), pp. S103–S147.
B. Li, S. Ma, and N. Wang:
Second-order convergence of the linearly extrapolated Crank–Nicolson method for the Navier-Stokes equations with H
^{1}
initial data
.
J. Sci. Comput.
88 (2021), article 70.
B. Li and S. Ma:
A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
.
J. Sci. Comput.
87 (2021), article 23.
G. Akrivis and B. Li:
Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation
.
IMA J. Numer. Anal.
(2020), DOI: 10.1093/imanum/draa065
G. Akrivis and B. Li:
Linearization of the finite element method for gradient flows by Newton’s method
.
IMA J. Numer. Anal.
(2020), DOI: 10.1093/imanum/draa016
B. Li, J. Yang, and Z. Zhou:
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
.
SIAM J. Sci. Comput.
42 (2020), pp. A3957–A3978.
B. Li, Y. Ueda, and G. Zhou:
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems
.
SIAM J. Numer. Anal.
58 (2020), pp. 2736–2763.
B. Li:
Convergence of Dziuk's linearly implicit parametric finite element method for curve shortening flow
.
SIAM J. Numer. Anal.
58 (2020), pp. 2315–2333.
B. Li, K. Wang, and Z. Zhou:
Long-time accurate symmetrized implicit-explicit BDF methods for a class of parabolic equations with non-selfadjoint operators
.
SIAM J. Numer. Anal.
58 (2020), pp. 189–210.
B. Li, J. Wang, and L. Xu:
A convergent linearized Lagrange finite element method for the magneto-hydrodynamic equations in 2D nonsmooth and nonconvex domains
.
SIAM J. Numer. Anal.
58 (2020), pp. 430–459.
B. Jin, B. Li, and Z. Zhou:
Subdiffusion with time-dependent coefficients: improved regularity and second-order time stepping
.
Numer. Math.
145 (2020), pp. 883-913.
W. Gong and B. Li:
Improved error estimates for semi-discrete finite element solutions of parabolic Dirichlet boundary control problems
.
IMA J. Numer. Anal.
40 (2020), no. 4, 2898–2939.
B. Jin, B. Li, and Z. Zhou:
Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint
.
IMA J. Numer. Anal.
40 (2020), pp. 377–404.
B. Kovács, B. Li, and C. Lubich:
A convergent algorithm for forced mean curvature flow driven by diffusion on the surface
.
Interfaces and Free Boundaries
22 (2020), pp. 443–464.
B. Li, K. Wang, and Z. Zhang:
A Hodge decomposition method for dynamic Ginzburg–Landau equations in nonsmooth domains -— a second approach
.
Commun. Comput. Phys.
28 (2020), pp. 768-802.
B. Li:
An explicit formula for corner singularity expansion of the solutions to the Stokes equations in a polygon
.
Int. J. Numer. Anal. Modeling
17 (2020), pp. 900-928.
G. Akrivis, B. Li, and D. Li:
Energy-decaying extrapolated RK-SAV methods for the Allen-Cahn and Cahn-Hilliard equations
.
SIAM J. Sci. Comput.
41 (2019), pp. A3703–A3727.
B. Kovács, B. Li, and C. Lubich:
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
.
Numer. Math.
143 (2019), pp. 797–853.
W. Cai, B. Li, Y. Lin, and W. Sun:
Analysis of fully discrete FEM for miscible displacement in porous media with Bear--Scheidegger diffusion tensor
.
Numer. Math.
141 (2019), pp. 1009–1042.
M. Gunzburger, B. Li, and J. Wang:
Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise
.
Numer. Math.
141 (2019), pp. 1043–1077.
M. Gunzburger, B. Li, and J. Wang:
Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise
.
Math. Comp.
88 (2019), pp. 1715–1741.
B. Jin, B. Li, and Z. Zhou:
Subdiffusion with a time-dependent coefficient: analysis and numerical solution
.
Math. Comp.
88 (2019), pp. 2157–2186.
B. Li:
Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra
.
Math. Comp.
88 (2019), pp. 1–44.
B. Li, J. Zhang, and C. Zheng:
Stability and error analysis for a second-order fast approximation of the one-dimensional Schrödinger equation under absorbing boundary conditions
.
SIAM J. Sci. Comput.
40 (2018), pp. A4083–A4104.
B. Li, J. Zhang and C. Zheng:
An efficient second-order finite difference method for the one-dimensional Schrödinger equation with absorbing boundary conditions
.
SIAM J. Numer. Anal.
56 (2018), pp. 766–791.
M. Gunzburger, X. He and B. Li:
On Stokes-Ritz projection and multi-step backward differentiation schemes in decoupling the Stokes-Darcy model
.
SIAM J. Numer. Anal.
56 (2018), pp. 397–427.
B. Jin, B. Li, and Z. Zhou:
Numerical analysis of nonlinear subdiffusion equations
.
SIAM J. Numer. Anal.
56 (2018), pp. 1–23.
W. Deng, B. Li, Z. Qian, and H. Wang:
Time discretization of the tempered fractional Feynman-Kac equation with measure data
.
SIAM J. Numer. Anal.
56 (2018), pp. 3249–3275
W. Deng, B. Li, W. Tian, and P. Zhang:
Boundary problems for the fractional and tempered fractional operators
.
Multiscale Model. Simul.
16 (2018), pp. 125–149.
K. Du, B. Li, W. Sun, and H. Yang:
Electromagnetic scattering from a cavity embedded in an impedance ground plane
.
Math. Methods in Applied Sciences
41 (2018), pp. 7748–7765.
P. C. Kunstmann, B. Li, and C. Lubich:
Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity
.
Found. Comput. Math.
18 (2018), pp. 1109–1130.
G. Akrivis and B. Li:
Maximum norm analysis of implicit-explicit backward difference formulae for nonlinear parabolic equations
.
IMA J. Numer. Anal.
38 (2018), pp. 75–101.
B. Jin, B. Li and Z. Zhou:
An analysis of the Crank-Nicolson method for subdiffusion
.
IMA J. Numer. Anal.
38 (2018), pp. 518–541.
B. Jin, B. Li, and Z. Zhou:
Discrete maximal regularity of time-stepping schemes for fractional evolution equations
.
Numer. Math.
138 (2018), pp. 101–131.
B. Jin, B. Li, and Z. Zhou:
Correction of high-order BDF convolution quadrature for fractional evolution equations
.
SIAM J. Sci. Comput.
39 (2017), pp. A3129–A3152.
B. Kovács, B. Li, C. Lubich and C. A. Power Guerra:
Convergence of finite elements on an evolving surface driven by diffusion on the surface
.
Numer. Math.
137 (2017), pp. 643–689.
B. Li, J. Liu and M. Xiao:
A new multigrid method for unconstrained parabolic optimal control problems
.
J. Comput. Appl. Math.
326 (2017), pp. 358–373.
B. Li and W. Sun:
Maximal L
^{p}
error analysis of FEMs for nonlinear parabolic equations with nonsmooth coefficients
.
Int. J. Numer. Anal. & Modeling
14 (2017), pp. 670–687.
B. Li and W. Sun:
Maximal regularity of fully discrete finite element solutions of parabolic equations
.
SIAM J. Numer. Anal.
55 (2017), pp. 521–542.
H. Gao, B. Li and W. Sun:
Stability and convergence of fully discrete Galerkin FEMs for the nonlinear thermistor equations in a nonconvex polygon
.
Numer. Math.
136 (2017), pp. 383–409.
G. Akrivis, B. Li and C. Lubich:
Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
.
Math. Comp.
86 (2017), pp. 1527–1552.
B. Li and Z. Zhang:
Mathematical and numerical analysis of time-dependent Ginzburg-Landau equations in nonconvex polygons based on Hodge decomposition
.
Math. Comp.
86 (2017), pp. 1579–1608.
B. Li and W. Sun:
Maximal L
^{p}
analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra
.
Math. Comp.
86 (2017), pp. 1071–1102.
B. Li:
Convergence of a decoupled mixed FEM for the dynamic Ginzburg–Landau equations in nonsmooth domains with incompatible initial data
.
Calcolo
54 (2017), pp. 1441–1480.
D. Leykekhman and B. Li:
Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions
.
Calcolo
54 (2017), pp. 541–565.
B. Li and C. Yang:
Global well-posedness of the time-dependent Ginzburg–Landau superconductivity model in curved polyhedra
.
J. Math. Anal. Appl.
451 (2017), pp. 102–116.
B. Kovács, B. Li and C. Lubich:
A-stable time discretizations preserve maximal parabolic regularity
.
SIAM J. Numer. Anal.
54 (2016), pp. 3600–3624.
B. Li and C. Yang:
Uniform BMO estimate of parabolic equations and global wellposedness of the thermistor problem
.
Forum of Mathematics, Sigma
3 (2015), e26. DOI:10.1017/fms.2015.29
B. Li, J. Liu and M. Xiao:
A fast and stable preconditioned iterative method for optimal control problem of wave equations
.
SIAM J. Sci. Comput.
37 (2015), pp. A2508–A2534.
B. Li:
Maximum-norm stability and maximal L
^{p}
regularity of FEMs for parabolic equations with Lipschitz continuous coefficients
.
Numer. Math.
131 (2015), pp. 489–516.
B. Li and W. Sun:
Regularity of the diffusion-dispersion tensor and error analysis of FEMs for a porous media flow
.
SIAM J. Numer. Anal.
53 (2015), pp. 1418–1437.
B. Li and Z. Zhang:
A new approach for numerical simulation of the time-dependent Ginzburg-Landau equations
.
J. Comput. Phys.
303 (2015), pp. 238–250.
K. Du, B. Li, W. Sun:
A numerical study on the stability of a class of Helmholtz problems
.
J. Comput. Phys.
287 (2015), pp. 46–59.
B. Li and W. Sun:
Linearized FE approximations to a nonlinear gradient flow (corrected version after publication, see page 11)
.
SIAM J. Numer. Anal.
52 (2014), pp. 2623–2646.
H. Gao, B. Li and W. Sun:
Optimal error estimates of linearized Crank-Nicolson Galerkin FEMs for the time-dependent Ginzburg-Landau equations in superconductivity
.
SIAM J. Numer. Anal.
52 (2014), pp. 1183–1202.
H. Gao, B. Li and W. Sun:
Unconditionally optimal error estimates of a Crank-Nicolson Galerkin method for the nonlinear thermistor equations
.
SIAM J. Numer. Anal.
52 (2014), pp. 933–954.
B. Li, J. Wang and W. Sun:
The stability and convergence of fully discrete Galerkin-Galerkin FEMs for porous medium flows
.
Commun. Comput. Phys.
15 (2014), pp. 1141–1158.
Z. Cao, B. Li and Y. Sun:
热方程的一些端点估计及其在Navier-Stokes方程中的应用
.
中国科学:数学
44 (2014), pp. 423–434.
B. Li and W. Sun:
Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media
.
SIAM J. Numer. Anal.
51 (2013), pp. 1959–1977.
B. Li and W. Sun:
Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
.
Int. J. Numer. Anal. & Modeling
10 (2013), pp. 622–633.
Y. Hou, B. Li and W. Sun:
Error estimates of splitting Galerkin methods for heat and sweat transport in textile materials
.
SIAM J. Numer. Anal.
51 (2013), pp. 88–111.
B. Li and W. Sun:
Numerical analysis of heat and moisture transport with a finite difference method
.
Numerical Methods for PDEs
29 (2013), pp. 226–250.
B. Li and W. Sun:
Global weak solution for a heat and sweat transport system in three-dimensional fibrous porous media with condensation/evaporation and absorption
.
SIAM J. Math. Anal.
44 (2012), pp. 1448–1473.
B. Li and W. Sun:
Heat-sweat flow in three-dimensional porous textile media
.
Nonlinearity
25 (2012), pp. 421-447.
Q. Zhang, B. Li and W. Sun:
Heat and sweat transport through clothing assemblies with phase changes, condensation/evaporation and absorption
.
Proc. Royal Society A
467 (2011), pp. 3469–3489.
C. Ye, B. Li and W. Sun:
Quasi-steady-state and steady-state models for heat and moisture transport in textile assemblies
.
Proc. Royal Society A
466 (2010), pp. 2875–2896.
B. Li and W. Sun:
Global existence of weak solution for nonisothermal multicomponent flow in porous textile media
.
SIAM J. Math. Anal.
42 (2010), pp. 3076–3102.
B. Li and W. Sun:
Newton-Cotes rules for Hadamard finite-part integrals on an interval
.
IMA J. Numer. Anal.
30 (2010), pp. 1235–1255.
B. Li, W. Sun, and Y. Wang:
Global existence of weak solution to the heat and moisture transport system in fibrous media
.
J. Differential Equations
249 (2010), pp. 2618–2642.