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