Buyang Li 李步扬
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
Education
PhD, City University of Hong Kong, 2012.
Research Interests
Numerical methods for PDEs, stability and convergence of numerical solutions
PDEs on surfaces, surface evolution under mean curvature flow and Willmore (elastic) flow
Incompressible Navier-Stokes equations
Energy diminishing methods for gradient flow of phase field models
Maximal $L^p$-regularity of time discretization methods
Analyticity, maximum-norm stability, and maximal $L^p$-regularity of finite element solutions to parabolic equations
Artificial boundary conditions/boundary integral equations for wave propagation in an unbounded domain
Dirichlet boundary control of parabolic equations
Fast preconditioned iterative method for optimal control of wave problems
High-order approximation of fractional evolution equations
Dynamic Ginzburg-Landau superconductivity equations in nonsmooth domains
Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity)
Modelling and computation of sweat transport in porous textile materials
Well-posedness of nonlinear PDEs
Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity)
Heat and moisture transport in fibrous media
Plenary/Main speaker in
第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议
, 山东曲阜, 9-11 August 2019
The 3rd Workshop on Numerical Methods for Fractional Derivative Problems
, Beijing Computational Science Research Center, 26-27 April 2019
Publications
B. Li:
Convergence of Dziuk's linearly implicit parametric finite element method for curve shortening flow
.
SIAM J. Numer. Anal.
2020
B. Jin, B. Li, and Z. Zhou:
Subdiffusion with time-dependent coefficients: improved regularity and second-order time stepping
.
Numer. Math.
2020, DOI: 10.1007/s00211-020-01130-2
D. Leykekhman and B. Li:
Weak discrete maximum principle of finite element methods in convex polyhedra
.
Math. Comp.
2020, DOI: 10.1090/mcom/3560
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.
2020, DOI: 10.1051/m2an/2020029
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, 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, 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:
Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint
.
IMA J. Numer. Anal.
40 (2020), pp. 377–404.
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.
W. Gong and B. Li:
Improved error estimates for semi-discrete finite element solutions of parabolic Dirichlet boundary control problems
.
IMA J. Numer. Anal.
(2019), DOI: 10.1093/imanum/drz029
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.