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

• J. Cao, B. Li, Y. Lin and F. Yao: Numerical approximation of discontinuous solutions of the semilinear wave equation.
  SIAM J. Numer. Anal., in press.
• G. Bai and B. Li: Convergence of a stabilized parametric finite element method of the Barrett-Garcke-Nürnberg type for curve shortening flow.
  Math. Comp., 70 pages, DOI: https://doi.org/10.1090/mcom/4019
• B. Li, S. Ma and W. Sun: Optimal analysis of finite element methods for the stochastic Stokes equations.
  Math. Comp. DOI: https://doi.org/10.1090/mcom/3972
• G. Bai, J. Hu and B. Li: A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field.
  SIAM J. Numer. Anal. 62 (2024), pp. 2172-2195.
• B. Li, W. Sun, Y. Xie and W. Yu: Optimal L² error analysis of a loosely coupled finite element scheme for thin-structure interactions.
  SIAM J. Numer. Anal. 62 (2024), pp. 1782-1813.
• B. Li, Z. Yang and Z. Zhou: High-order splitting finite element methods for the subdiffusion equation with limited smoothing property.
  Math. Comp. 93 (2024), pp. 2557-2586.
• B. Li, W. Qiu, Y. Xie and W. Yu: Weak discrete maximum principle of isoparametric finite element methods in curvilinear polyhedra.
  Math. Comp. 93 (2024), pp. 1-34.
• B. Duan and B. Li: New artificial tangential motions for parametric finite element approximation of surface evolution.
  SIAM J. Sci. Comput. 46 (2024), pp. A587-A608.
• G. Bai, J. Hu and B. Li: High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation.
  SIAM J. Sci. Comput. 46 (2024), pp. A1026-A1046.
• W. Gong, B. Li and Q. Rao: Convergent evolving finite element approximations of boundary evolution under shape gradient flow.
  IMA J. Numer. Anal. 44 (2024), pp. 2667-2697.
• J. Cao, B. Li and Y. Lin: A new second-order low-regularity integrator for the cubic nonlinear Schrödinger equation.
  IMA J. Numer. Anal. 44 (2024), pp. 1313–1345.
• B. Li, J. Shen, Z. Yang and Y. Zhang: Efficient energy stable schemes for incompressible flows with variable density.
  J. Comput. Phys. 517 (2024), article 113365.

• B. Li, Y. Li and Z. Yang: An optimized CIP-FEM to reduce the pollution errors for the Helmholtz equation on a general unstructured mesh.
  J. Comput. Phys. 511 (2024), article 113120.
• G. Bai and B. Li: A new approach to the analysis of parametric finite element approximations to mean curvature flow.
  Found. Comput. Math. (2023), 64 pages, DOI: https://doi.org/10.1007/s10208-023-09622-x
• B. Li, Y. Li and W. Zheng: A new perfectly matched layer method for the Helmholtz equation in nonconvex domains.
  SIAM J. Appl. Math. 83 (2023), pp. 666-694.
• B. Li, Y. Lin, S. Ma and Q. Rao: An exponential spectral method using VP means for semilinear subdiffusion equations with rough data.
  SIAM J. Numer. Anal. 61 (2023), pp. 2305-2326.
• G. Bai and B. Li: Erratum: Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements.
  SIAM J. Numer. Anal. 61 (2023), pp. 1609-1612.
• B. Li, H. Li and Z. Yang: Convergent finite element methods for the perfect conductivity problem with close-to-touching inclusions.
  IMA J. Numer. Anal. (2023), https://doi.org/10.1093/imanum/drad088
• B. Li, Y. Xia and Z. Yang: Optimal convergence of arbitrary Lagrangian--Eulerian iso-parametric finite element methods for parabolic equations in an evolving domain.
  IMA J. Numer. Anal. 43 (2023), pp. 501–534.
• G. Bai, B. Li and Y. Wu: A constructive low-regularity integrator for the 1d cubic nonlinear Schrödinger equation under the Neumann boundary condition.
  IMA J. Numer. Anal. 43 (2023), pp. 3243–3281.
• B. Kovács and B. Li: Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems.
  IMA J. Numer. Anal. 43 (2023), pp. 1937–1969.
• B. Li, K. Schratz and F. Zivcovich: A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation.
  ESAIM: Math. Model. Numer. Anal. 57 (2023), pp. 899-919.
• X. Gui, B. Li and J. Wang: Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data.
  Sci. China Math. (2023), https://doi.org/10.1007/s11425-022-2157-2
• J. Hu and B. Li: Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow.
  Numer. Math. 152 (2022), pp. 127–181.
• B. Li: Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh.
  Math. Comp. 91 (2022), pp. 1533–1585.
• B. Li, S. Ma and K. Schratz: A semi-implicit exponential low-regularity integrator for the Navier-Stokes equations.
  SIAM J. Numer. Anal. 60 (2022), pp. 2273–2292.
• B. Li and S. Ma: Exponential convolution quadrature for nonlinear subdiffusion equations with nonsmooth initial data.
  SIAM J. Numer. Anal. 60 (2022), pp. 503–528.
• X. Gui, B. Li and J. Wang: Convergence of renormalized finite element methods for heat flow of harmonic maps.
  SIAM J. Numer. Anal. 60 (2022), pp. 312–338.
• B. Li: Maximal regularity of multistep fully discrete finite element methods for parabolic equations.
  IMA J. Numer. Anal. 42 (2022), pp. 1700–1734.
• B. Li, S. Ma and Y. Ueda: Analysis of fully discrete finite element methods for 2D Navier-Stokes equations with critical initial data.
  ESAIM: Math. Model. Numer. Anal. 56 (2022), pp. 2105–2139.
• B. Duan, B. Li and Z. Yang: An energy diminishing arbitrary Lagrangian–Eulerian finite element method for two-phase Navier–Stokes flow.
  J. Comput. Phys. 461 (2022), article 111215.
• M. D. Gunzburger, B. Li, J. Wang and Z. Yang: A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere.
  J. Comput. Phys. 457 (2022), article 111067.
• H. Hu, B. Li and J. Zou: Optimal convergence of the Newton iterative Crank–Nicolson finite element method for the nonlinear Schrödinger equation.
  Comput. Methods Appl. Math. 22 (2022), pp. 591–612.
• W. Gong, B. Li and H. Yang: Optimal control in a bounded domain for wave propagating in the whole space: coupling through boundary integral equations.
  J. Sci. Comput. 92 (2022), article 91.
• B. Li, W. Qiu and Z. Yang: A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density.
  J. Sci. Comput. 91 (2022), article 2.
• B. Li: 曲率流的参数化有限元逼近. 计算数学 44 (2022), pp. 145–162.
• B. Kovács, B. Li and C. Lubich: A convergent evolving finite element algorithm for Willmore flow of closed surfaces.
  Numer. Math. 149 (2021), pp. 595–643.
• 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: 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.
  
  G. Bai and B. Li: Erratum: Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements. SINUM 61 (2023), pp. 1609-1612.
• 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 H¹ 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.
• B. Duan, B. Li and Z. Zhang: High-order fully discrete energy diminishing evolving surface finite element methods for a class of geometric curvature flows.
  Ann. Appl. Math. 37 (2021), pp. 405-436.
• 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: https://doi.org/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: https://doi.org/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.