- 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

- 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 L
^{2}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 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. - 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.