Publications

• In Refereed Journals (submitted, accepted or published)
  
  
  • 54) H. Wang , F. Li, C.-W. Shu, Q. Zhang, Uniform stability for local discontinuous Galerkin methods with implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation, submitted (2022)
  
  
  • 53) M. Lyu, V.A. Bokil, Y. Cheng, F. Li, Energy stable nodal DG methods for Maxwell's equations of mixed-order form in nonlinear optical media, [preprint], submitted (2022)
  
  
  • 52) D. Appelo, L. Zhang, T Hagstrom, F. Li, An energy-based discontinuous Galerkin method with tame CFL numbers for the wave equation [preprint], submitted (2022)
  
  
  • 51) Z. Peng, M. Wang, F. Li, A learning-based projection method for model order reduction of transport problems [PDF], Journal of Computational and Applied Mathematics, v418 (2023), doi.org/10.1016/j.cam.2022.114560
  
  
  • 50) Z. Peng, Y. Chen, Y. Cheng, F. Li, A reduced basis method for radiative transfer equation, [PDF], Journal of Scientific Computing, v91 (2022), doi.org/10.1007/s10915-022-01782-2 (Special issue dedicated to the ICERM Spring 2020 semester program on Model Order Reduction)
  
  
  • 49) M. Lyu, V.A. Bokil, Y. Cheng, F. Li, Energy stable nodal discontinuous Galerkin methods for nonlinear Maxwell's equations in multi-dimensions, [PDF], Journal of Scientific Computing, v89 (2021), https://doi.org/10.1007/s10915-021-01651-4
  
  
  • 48) Z. Peng and F. Li, Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement, [PDF], SIAM Journal on Scientific Computing, v43 (2021), pp.A1194-A1220
  
  
  • 47) Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property, [PDF], SIAM Journal on Numerical Analysis, v59 (2021), pp.925-954
  
  
  • 46) Z. Peng, Y. Cheng, J.-M. Qiu, F. Li, Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling, [PDF], Journal of Computational Physics, v415 (2020), pp.109485
  
  
  • 45) Z. Peng, V.A. Bokil, Y. Cheng, F. Li, Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension, [PDF], Journal of Computational Physics, v402 (2020), pp.109101
  
  
  • 44) D. Appelo, V.A. Bokil, Y. Cheng, F. Li, Energy stable SBP-FDTD methods for Maxwell-Duffing models in nonlinear photonics, [PDF], IEEE Journal on Multiscale and Multiphysics Computational Techniques, v4 (2019), pp.329-336
  
  
  • 43) Y. Jiang, P. Sakkaplangkul, V.A. Bokil, Y. Cheng, F. Li, Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media [PDF], Journal of Computational Physics, v394 (2019), pp.100-135
  
  
  • 42) A. Chen, F. Li, Y. Cheng, An ultra-weak discontinuous Galerkin method for Schrodinger equation in one dimension, [PDF], Journal of Scientific Computing, v78 (2019), pp.772-815
  
  
  • 41) P. Fu, Y. Cheng, F. Li, Y Xu, Discontinuous Galerkin methods with optimal L2 accuracy for one dimensional linear PDEs with high order spatial derivatives, [PDF], Journal of Scientific Computing, v78 (2019), pp.816-863
  
  
  • 40) V.A. Bokil, Y. Cheng, Y. Jiang, F. Li, P. Sakkaplangkul, High spatial order energy stable FDTD methods for Maxwell's equations in nonlinear optical media in one dimension, [PDF], Journal of Scientific Computing, v77 (2018), pp.330-371
  
  
  • 39) P. Fu, F. Li, Y. Xu, Globally divergence-free discontinuous Galerkin methods for ideal Magnetohydrodynamic equations, [PDF], Journal of Scientific Computing, v77 (2018), pp.1621-1659
  
  
  • 38) V. A. Bokil, Y. Cheng, Y. Jiang, F. Li, Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media, [PDF], Journal of Computational Physics, v350 (2017), pp.420-452
  
  
  • 37) H. Yang and F. Li, Discontinuous Galerkin methods for relativistic Vlasov-Maxwell system, [PDF], Journal of Scientific Computing, v73 (2017), pp.1216-1248
  
  
  • 36) M. Li, P. Guyenne, F. Li, L. Xu, A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations, [PDF], Journal of Scientific Computing, v71 (2017), pp.994-1034
  
  
  • 35) Y. Cheng, C.-S. Chou, F. Li, Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations, [PDF], Mathematics of Computation, v86 (2017), pp.121-155.
  
  
  • 34) M. Li, F. Li, Z. Li, L. Xu, Maximum-principle-satisfying and positivity-preserving high order central DG methods for hyperbolic conservation laws, [PDF], SIAM Journal on Scientific Computing, v38 (2016), pp.A3720-A3740
  
  
  • 33) Z. Tao, F. Li, J. Qiu, High-order central Hermite WENO schemes: dimension-by-dimension moment-based reconstructions, [PDF], Journal of Computational Physics, v318 (2016), pp.222-251
  
  
  • 32) F. Long, F. Li, X. Intes, S.P. Kotha, Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method, [PDF], The Journal of Biomedical Optics, v21 (2016), 036003
  
  
  • 31) H. Yang and F. Li, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, [PDF], ESAIM: Mathematical Modelling and Numerical Analysis, v50 (2016), pp.965-993
  
  
  • 30) Z. Tao, F. Li, J. Qiu, High-order central Hermite WENO schemes for hyperbolic conservation laws, [PDF], Journal of Computational Physics, v281 (2015), pp.148-176
  
  
  • 29) T. Xiong, J. Jang, F. Li, J.-M. Qiu, High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation, [PDF], Journal of Computational Physics, v284 (2015), pp.70-94
  
  
  • 28) J. Jang, F. Li, J.-M. Qiu, T. Xiong, High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling, [PDF], Journal of Computational Physics, v281 (2015), pp.199-224
  
  
  • 27) M.A. Reyna and F. Li, Operator bounds and time step conditions for DG and central DG methods, [PDF], Journal of Scientific Computing, v62 (2015), pp.532-554 (Note: correction is made to definition 9 on page 10)
  
  
  • 26) J. Gopalakrishnan, F. Li, N.-C. Nguyen, J. Peraire, Spectral approximations by the HDG method, [PDF], Mathematics of Computation, v84 (2015), pp.1037-1059.
  
  
  • 25) H. Yang and F. Li, Error estimates of Runge-Kutta discontinuous Galerkin methods for the Vlasov-Maxwell system, [PDF], ESAIM: Mathematical Modelling and Numerical Analysis, v49 (2015), pp.69-99.
  
  
  • 24) J. Jang, F. Li, J.-M. Qiu, T. Xiong, Analysis of asymptotic preserving DG-IMEX schemes for linear kinetic transport equations in a diffusive scaling, [PDF], SIAM Journal on Numerical Analysis, v52 (2014), pp. 1497-2206
  
  
  • 23) M. Li, P. Guyenne, F. Li, L. Xu, High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model, [PDF], Journal of Computational Physics, v257 (2014), pp.169-192
  
  
  • 22) Y(ingda). Cheng, I. Gamba, F. Li, P. Morrison, Discontinuous Galerkin methods for Vlasov-Maxwell equations, [PDF], SIAM Journal on Numerical Analysis, v52-2 (2014), pp. 1017-1049 (see arxiv:1302.2136 for a long version)
  
  
  • 21) H. Yang, F. Li, J. Qiu, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, [PDF], Journal of Scientific Computing, v55 (2013), pp.552-574
  
  
  • 20) Y(ue). Cheng, F. Li, J. Qiu, L. Xu, Positivity-preserving DG and central DG methods for ideal MHD equations, [PDF], Journal of Computational Physics, v238 (2013), pp.255-280
  
  
  • 19) S. Yakovlev, L. Xu, F. Li, Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Science, v4 (2013), pp.80-91. (Special issue on Computational Methods for Hyperbolic Problems)
  
  
  • 18) F. Li and L. Xu, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Physics, v231 (2012), pp.2655-2675
  
  
  • 17) F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method, [PDF], Journal of Scientific Computing, v51 (2012), pp.213-223
  
  
  • 16) F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, [PDF], Journal of Computational Physics, v230 (2011), pp.4828-4847. (Correction: in section 4.2.6, it is `with the darker area representing the smaller value)
  
  
  • 15) W. Guo, F. Li, J. Qiu, Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, v47 (2011), pp.239-257
  
  
  • 14) Y.-T. Zhang, S. Chen, F. Li, H.-K. Zhao, C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations, [PDF], SIAM Journal on Scientific Computing, v33 (2011), pp.1873-1896
  
  
  • 13) B. Cockburn, J. Gopalakrishnan, F. Li, N.-C. Nguyen, J. Peraire, Hybridization and postprocessing techniques for mixed eigenfunctions, [PDF] , SIAM Journal on Numerical Analysis, v48 (2010), pp.857-881
  
  
  • 12) F. Li and S. Yakovlev, A central discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, v45 (2010), pp.404-428. (Special issue in memory of Professor David Gottlieb)
  
  
  • 11) S. C. Brenner, F. Li, L.-Y. Sung, Nonconforming Maxwell eigensolvers, [PDF], Journal of Scientific Computing, v40 (2009), pp.51-85
  
  
  • 10) S. C. Brenner, F. Li, L.-Y. Sung, A nonconforming penalty method for a two-dimensional curl-curl problem, [PDF], Mathematical Models and Methods in Applied Mathematics, v19 (2009), pp.651-668
  
  
  • 9) F. Li, C.-W. Shu, Y.-T. Zhang, H.-K. Zhao, A second order DGM based fast sweeping method for Eikonal equations, [PDF] Journal of Computational Physics, v227 (2008), pp.8191-8208
  
  
  • 8) S. C. Brenner, J. Cui, F. Li, L.-Y. Sung, A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem, [PDF]  Numerische Mathematik, v109 (2008), pp.509-533
  
  
  • 7) S. C. Brenner, F. Li, L.-Y. Sung, A locally divergence-free interior penalty method for two-dimensional curl-curl problems, [PDF]  SIAM Journal on Numerical Analysis, v46 (2008), pp.1190-1211
  
  
  • 6) S. C. Brenner, F. Li, L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Mathematics of Computation, v76 (2007), pp.573-595
  
  
  • 5) F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation, [PDF]  [Some Correction] Methods and Applications of Analysis, v13 (2006), pp.215-233 (Special issue dedicated to Professor Bjorn Engquist on the occasion of his 60th birthday)
  
  
  • 4) F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF]  Applied Mathematics Letters, v18 (2005), pp.1204-1209
  
  
  • 3) F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations, [PDF]  Journal of Scientific Computing, v22-23 (2005), pp.413-442
  
  
  • 2) B. Cockburn, F. Li, C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, [PDF]  Journal of Computational Physics, v194 (2004), pp.588-610
  
  
  • 1) L.-A. Ying and F. Li, Exterior Problem of the Darwin Model and its Numerical Computation, [PDF]  ESAIM: Mathematical Modelling and Numerical Analysis, v37 (2003), pp.515-532
  
  
• Refereed Book Chapters
  
  
  • B1) Y. Chen, Z. Chen, Y. Cheng, A. Gillman, and F. Li, Study of discrete scattering operators for some linear kinetic models, [PDF], The IMA Volumes in Mathematics and its Applications, Vol. 160 (2016), Susanne Brenner (Ed): Topics in Numerical Partial Differential Equations and Scientific Computing, pp.99-136, Springer.
  
  
• Publications in Conference and Workshop Proceedings
  
  
  • [2] S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Proceedings of the joint Workshop by AWM and MSRI: The Legacy of Ladyzhenskaya and Oleinik, 2006, pp.187-191
  
  
  • [1] B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results, the proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, Editor, June 2003, Elsevier Science, pp.1900-1902
  
  
• Research report
  
  
  • F. Li, A priori error estimates of a local-structure-preserving LDG method, [PDF], May 2011