Ruo Li

中文版

Textbooks:

  1. 李若，卢朓 编著，《北太天元科学计算编程与应用》，北京大学出版社，2025。

  2. 汤涛，李若，张争茹 著，《偏微分方程的移动网格方法》，科学出版社， 信息与计算科学丛书(92)，2023。

  3. 张林波，迟学斌，莫则尧，李若 编著，《并行计算导论》，清华大学出版社， 2006。

Journal and Proceeding Papers:

    Submitted:

  1. M.-S. Huang, R. Li, K. Yan, C.-B. Yao and W.-J. Ying,
    An Efficient Monte Carlo Simulation for Thermal Radiative Transfer Based on Global Optimal Reference Field,
    arXiv: 2411.02415

  2. G.-H. Hu, R. Li and H.-F. Zhan,
    A gradient flow model for ground state calculations in Wigner formalism based on density functional theory,
    arXiv: 2409.10851

  3. R. Li, Q.-C. Liu and F.-Y. Yang,
    A Preconditioned Discontinuous Galerkin Method for Biharmonic Equation with C^0-Reconstructed Approximation,
    arXiv: 2407.03793

  4. R. Li, Q.-C. Liu and S.-H. Zhao,
    An arbitrary order Reconstructed Discontinuous Approximation to Fourth-order Curl Problem,
    arXiv: 2406.05624

  5. R. Li, W.-M. Li, S.-T. Liang, Y.-H. Shao, M. Tang and Y.-L. Wang,
    An asymptotic-preserving method for the three-temperature radiative transfer model,
    arXiv: 2402.19191

  6. Z.-Y. Jin and R. Li,
    Lax Equivalence for Hyperbolic Relaxation Approximations,
    arXiv: 2311.10662

    7. Accepted:

    Published:

  7. 李若,
    从玻尔兹曼方程到宏观流体力学模型,
    《中国数学会通讯》，总第171期，2024(3)，pp. 48-57。
    PDF 下载

  8. R. Li and W. Zhong,
    Preventing numerical oscillations in the efficient component-wise WENO-ACM method for compressible flows with discontinuities,
    Computational and Applied Mathematics, 44:90, 2025
    DOI: 10.1007/s40314-024-03051-4

  9. R. Li, Y.-X. Lu and Y.-L. Wang,
    A highly efficient asymptotic preserving IMEX method for the quantum BGK equation,
    Journal of Computational Physics, 522(2025) 113619.
    DOI: 10.1016/j.jcp.2024.113619
    arXiv: 2312.16585

  10. R. Li and W. Zhong,
    An Improved WENO-Z+ Scheme,
    Advances in Applied Mathematics and Mechanics, 17(1), pp.31-68. February 2025
    DOI: 10.4208/aamm.OA-2022-0308

    11. 2025

  11. R. Li, Q.-C. Liu and S.-H. Zhao,
    A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations,
    Advances in Applied Mathematics and Mechanics, online.
    DOI: 10.4208/aamm.OA-2024-0086
    arXiv: 2407.07629

  12. Z.-Y. Jin and R. Li,
    Natural Model Reduction for Kinetic Equations,
    Research in Mathematical Sciences, Volume 11, article number 53, 03 August 2024.
    DOI: 10.1007/s40687-024-00466-7
    arXiv: 2310.12799

  13. Z.-N. Cai, Y. Chen, Y.-N. Di, G.-H. Hu, R. Li, W.-B. Liu, H.-Y. Wang, F.-Y. Yang, C.-B. Yao and H.-F. Zhan,
    AFEPack: a general-purpose C++ library for numerical solutions of partial differential equations,
    Communications in Computational Physics, July 2024, Vol. 36, No. 1, pp. 274-318.
    DOI: 10.4208/cicp.OA-2024-0027

  14. R. Li, Q.-C. Liu and F.-Y. Yang,
    Preconditioned NonSymmetric/Symmetric Discontinuous Galerkin Method for Elliptic Problem with Reconstructed Discontinuous Approximation,
    Journal of Scientific Computing, 06 August 2024, 100:88
    DOI: 10.1007/s10915-024-02639-6
    arXiv: 2306.15420

  15. Y. Wang, R. Li, Y.-L. Wang and G.-X. Ni,
    A Strang-splitting based unified gas-kinetic scheme for two species plasma in spherical coordinate,
    Computers & Fluids, Volume 266, 15 November 2023, 106052
    DOI: 10.1016/j.compfluid.2023.106052

  16. R. Li and Y.-C. Yang,
    On Well-posed Boundary Conditions for the Linear Non-homogeneous Moment Equations in Half-space,
    Journal of Statistical Physics, 190:185, 2023
    DOI: 10.1007/s10955-023-03186-4
    arXiv: 2209.04629

    17. 2024

  17. R. Li, Y.-X. Lu, Y.-L. Wang,
    Hermite spectral method for the inelastic Boltzmann equation,
    Physics of Fluids, 10-02-2023(online), Vol.35, Issue 10, 2023
    DOI: 10.1063/5.0172157
    arXiv: 2301.05850

  18. G.-H. Hu, R. Li and X.-C. Meng,
    A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme,
    Advances in Applied Mathematics and Mechanics, online, July 2023.
    DOI: 10.4208/aamm.OA-2022-0267

  19. J.-T. Huang, R. Li and Y.-Z. Zhou,
    Coupling conditions for linear hyperbolic relaxation systems in two-scales problems,
    Mathematics of Computation, 92(343), September 2023, pp. 2133-2165
    DOI: 10.1090/mcom/3845
    arXiv: 2207.06639

  20. Y. Chen, R. Li and Q.-C. Liu,
    An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem,
    Annuals of Applied Mathematics, 2023-06-14 online.
    DOI: 10.4208/aam.OA-2023-0011
    arXiv: 2305.03430

  21. R. Li, Y.-C. Yang and Y.-Z. Zhou,
    Construction of boundary conditions for Navier-Stokes equations from the moment system,
    Journal of Statistical Physics, 190, Article number: 104 (May 2023).
    DOI: 10.1007/s10955-023-03115-5
    arXiv: 2209.10344

  22. R. Li, Q.-C. Liu and F.-Y. Yang,
    A Reconstructed Discontinuous Approximation on Unfitted Meshes to H(curl) and H(div) Interface Problems,
    Computer Methods in Applied Mechanics and Engineering, January 2023, 403(3):115723
    DOI: 10.1016/j.cma.2022.115723

  23. R. Li, Q.-C. Liu and F.-Y. Yang,
    A Discontinuous Least Squares Finite Element Method for The Helmholtz Equation,
    Numerical Methods for Partial Differential Equations, 39（2), March 2023, pp. 1425-1448
    DOI: 10.1002/num.22940
    arXiv: 2105.01909

  24. R. Li and F.-Y. Yang,
    Reconstructed Discontinuous Approximation to Stokes Equation in A Sequential Least Squares Formulation,
    Journal of Computational Mathematics, 2023, 41(1), pp. 39-71.
    DOI: 10.4208/jcm.2104-m2020-0231
    arXiv: 2003.01930

  25. R. Li and F.-Y. Yang,
    A Reconstructed Discontinuous Approximation to Monge-Ampere Equation in Least Square Formation,
    Advances in Applied Mathematics and Mechanics, 2022-10-12 online.
    DOI: 10.4208/aamm.OA-2022-0047
    arXiv: 1912.05822

  26. R. Li and Y.-C. Yang,
    Linear Moment Models to Approximate Knudsen Layers,
    International Journal of Numerical Analysis and Modeling, 20 (2023), pp. 153-175.
    DOI: 10.4208/ijnam2023-1007
    arXiv: 2204.04941

  27. W.-Z. Huang, R. Li, J.-X. Qiu and M. Zhang,
    A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes,
    Journal of Computational Physics, Volume 487, 15 August 2023, 112147
    DOI: 10.1016/j.jcp.2023.112147
    arXiv: 2205.14560

  28. R. Li and Y.-C. Yang,
    Slip and Jump Coefficients for General Gas-Surface Interactions According to the Moment Method,
    Physics of Fluids, Volume 35, 032010, 2023.
    DOI: 10.1063/5.0142861
    arXiv: 2301.12177

  29. R. Li and W. Zhong,
    Locally Order-Preserving Mapping for WENO Methods,
    Journal of Computational and Applied Mathematics, Volume 424, 1 May 2023, 115004.
    DOI: 10.1016/j.cam.2022.115004
    arXiv: 2110.01373

  30. R. Li and W. Zhong,
    A robust and efficient component-wise WENO scheme for Euler equations,
    Applied Mathematics and Computation, Vol. 438, 1 February 2023, 127583
    DOI: 10.1016/j.amc.2022.127583

    31. 2023

  31. R. Li and W. Zhong,
    An Improved Component-Wise WENO-NIP Scheme for Euler System,
    Mathematics 2022, 10(20), 3881
    DOI: 10.3390/math10203881

  32. R.Li, Y.-X. Lu, Y.-L. Wang and H.-X. Xu,
    Hermite spectral method for multi-species Boltzmann equation,
    Journal of Computational Physics, Vol. 471 (2022) 111650.
    DOI: 10.1016/j.jcp.2022.111650

  33. R. Li and W. Zhong,
    An extension of the order-preserving mapping to the WENO-Z-type schemes,
    Advances in Applied Mathematics and Mechanics, 2022, Online First.
    DOI: 10.4208/aamm.OA-2022-0032
    arXiv: 2210.13607

  34. R. Li, Q.-C. Liu and F.-Y. Yang,
    A discontinuous least squares finite element method for time-harmonic Maxwell equations,
    IMA Journal of Numerical Analysis, 42, 2022, pp. 835-860.
    DOI: 10.1093/imanum/draa094
    arXiv: 2007.06791

  35. R. Li and W. Zhong,
    A general improvement in the WENO-Z-type schemes,
    Communications in Computational Physics, 31(5), 2022, pp. 1362-1401.
    DOI: 10.4208/cicp.OA-2021-0202
    arXiv: 2202.12718

  36. Z.-Y. Jin and R. Li,
    High Order Numerical Homogenization for Dissipative Ordinary Differential Equations,
    Multiscale Modelling and Simulation, 20(2), 2022, pp. 583-617
    DOI: 10.1137/21M1397003
    arXiv: 2102.03527

  37. R. Li and W. Zhong,
    A new mapped WENO scheme using order-preserving mapping,
    Communications in Computational Physics, 31(2), 2022, pp. 548-592.
    DOI: 10.4208/cicp.OA-2021-0150
    arXiv: 2104.04467

  38. R. Li and W. Zhong,
    An efficient mapped WENO scheme using approximate constant mapping,
    Numerical Mathematics: Theory, Method and Applications, 15(1), 2022, pp. 1-41.
    DOI: 10.4208/nmtma.OA-2021-0074
    arXiv: 2102.00231

  39. Z.-N. Cai, Y.-W. Fan and R. Li,
    Hyperbolic Model Reduction for Kinetic Equations,
    In: Chacón Rebollo, T., Donat, R., Higueras, I. (eds) Recent Advances in Industrial and Applied Mathematics. SEMA SIMAI Springer Series, vol 1. Springer, Cham. 07 April 2022.
    DOI: 10.1007/978-3-030-86236-7_8
    arXiv: 2001.10370

  40. R. Li and W. Zhong,
    Improvement of the WENO-NIP Scheme for Hyperbolic Conservation Laws,
    Axioms: Numerical Computation, Approximation of Functions and Applied Mathematics, 2022, 11(5), 190,
    DOI: 10.3390/axioms11050190


    41. 2022

  41. R. Li and W. Zhong,
    A modified adaptive improved mapped WENO method,
    Communications in Computational Physics, 30(5), 2021, pp. 1545-1588.
    DOI: 10.4208/cicp.OA-2021-0057
    arXiv: 2011.03916

  42. R. Li, W.-M. Li and L.-C. Zheng,
    Direct Flux Gradient Approximation to Close Moment Model for Kinetic Equations,
    SIAM Journal on Applied Mathematics, 81(5), 2021, 2153-2179.
    DOI: 10.1137/21M1396836.
    arXiv: 2102.07641

  43. G.-H. Hu, R. Li and X.-H. Zhang,
    A novel stabilized Galerkin meshless method for steady incompressible Navier-Stokes equations,
    Journal Engineering Analysis with Boundary Elements, Volume 133, 1 December 2021, Pages 95-106.
    DOI: 10.1016/j.enganabound.2021.08.017

  44. R. Li, P. Song and L.-C. Zheng,
    A Nonlinear Moment Model for Radiative Transfer Equation,
    Multiscale Modelling and Simulation, 19(3), 2021, 1425-1452.
    DOI: 10.1137/20M1341155.
    arXiv: 2005.13142

  45. R. Li and W. Zhong,
    Towards building the OP-Mapped WENO schemes: A general methodology,
    Mathematical and Computational Applications, 2021, 26, 67, PDF online
    DOI: 10.3390/mca26040067
    arXiv: 2105.04783

  46. R. Li and F.-Y. Yang,
    A sequential least squares method for elliptic equations in non-divergence form,
    Numerical Mathematics: Theory, Method and Applications, online July 26, 2021
    DOI: 10.4208/nmtma.OA-2021-0042
    arXiv: 1906.03754

  47. R. Li, Y.-N. Ren, Y.-L. Wang,
    Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma,
    Journal of Computational Physics, Volume 434, 1 June 2021, 110235.
    arXiv: 2004.06484

  48. Y.-N. Di, G.-H. Hu, R. Li and F. Yang,
    On Accurately Resolving Detonation Dynamics by Adaptive Finite Volume Method on Unstructured Grids,
    Communications in Computational Physics, 29 (2021), pp. 445-471.
    DOI: 10.4208/cicp.OA-2020-0028

    49. 2021

  49. Y.-W. Fan, R. Li and L.-C. Zheng,
    A Nonlinear Hyperbolic Model for Radiative Transfer Equation in Slab Geometry,
    SIAM Journal on Applied Mathematics, 80(6), 2020, pp. 2388-2419.
    DOI: 10.1137/19M126774X
    arXiv: 1911.05472

  50. L. Chen, R. Li and F. Yang,
    An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions,
    CSIAM Trans. Appl. Math., 1 (2020), pp. 491-517.
    arXiv: 1706.01361

  51. R. Li, Y.-L. Wang and Y.-X. Wang,
    Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation,
    SIAM Journal on Scientific Computing, 42(3), 2020, pp. B792-B815.
    DOI: 10.1137/18M1230268

  52. R. Li and F.-Y. Yang,
    A Discontinuous Galerkin Method by Patch Reconstruction for Elliptic Interface Problem on Unfitted Mesh,
    SIAM Journal on Scientific Computing, 42(2), 2020, pp. A1428-A1457.
    DOI: 10.1137/19M1290528

  53. R. Li and F.-Y. Yang,
    A Least Squares Method for Linear Elasticity using A Patch Reconstructed Space,
    Computer Methods in Applied Mechanics and Engineering, 363(2020), 112902.
    DOI: 10.1016/j.cma.2020.112902

  54. R. Li and X.-H. Zhang,
    A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids,
    Numerical Mathematics: Theory, Method and Applications, Vol.13, No. 2,2020, pp. 479-496.
    DOI: 10.4208/nmtma.OA-2019-0080

  55. L. Chen, R. Li and C.-B. Yao,
    An Approximate Riemann Solver for Fluid-Solid Interaction Problems with Mie-Grüneisen Equationsof State,
    Communications in Computational Physics, Vol.27, No. 3, 2020, pp. 861-896.
    DOI: 10.4208/cicp.OA-2018-0250

  56. R. Li and F.-Y. Yang,
    A Sequential Least Squares Method for Poisson Equation using A Patch Reconstructed Space,
    SIAM Journal on Numerical Analysis 58(1), 2020, pp. 353-374.
    DOI: 10.1137/19M1239593

  57. R. Li, Y.-L. Wang and C.-B. Yao,
    A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums,
    Advances in Applied Mathematics and Mechanics, 12 (2020), pp. 212-250.
    DOI: 10.4208/aamm.OA-2019-0039

    58. 2020

  58. R. Li, Z.-Y. Sun and Z.-J. Yang,
    A Discontinuous Galerkin Method for the Stokes Equation by Divergence-free Patch Reconstruction,
    Numerical Methods for Partial Differential Equations, 36, 2020, pp. 756-771.
    DOI: 10.1002/num.22449

  59. R. Li, W.-M. Li and L.-C. Zheng,
    A Nonlinear Three-Moment Model for Radiative Transfer in Spherical Symmetry,
    Mathematics and Computers in Simulation, Volume 170, April 2020, pp. 285-299.
    DOI: 10.1016/j.matcom.2019.11.004

  60. Y.-W. Fan, R. Li and L.-C. Zheng,
    A Nonlinear Moment Model for Radiative Transfer Equation in Slab Geometry,
    Journal of Computational Physics, Volume 404, 1 March 2020, 109128.
    DOI: 10.1016/j.jcp.2019.109128

  61. R. Li, Z.-Y. Sun and F.-Y. Yang,
    Solving Eigenvalue Problems in a Discontinuous Approximation Space by Patch Reconstruction,
    SIAM Journal on Scientific Computing, Vol. 41, Issue 5, pp. A3381-A3400.
    DOI: 10.1137/19M123693X.

  62. R. Li and W.-M. Li,
    3D B2 Model for Radiative Transfer Equation,
    International Journal of Numerical Analysis and Modeling, 17(1), pp. 118-150, 2019.

  63. R. Li, P.-B. Ming, Z.-Y. Sun and Z.-J. Yang,
    An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element,
    Journal of Scientific Computing, Vol.80, 2019, pp. 268-288.
    DOI:10.1007/s10915-019-00937-y

  64. R. Li, P.-B. Ming, Z.-Y. Sun, F.-Y. Yang and Z.-J. Yang,
    A discontinuous Galerkin method by patch reconstruction for biharmonic problem,
    Journal of Computational Mathematics, Vol.37, No.4, 2019, pp. 524-540.
    DOI:10.4208/jcm.1807-m2017-0276

  65. Y.-W. Fan, J. Li, R. Li and Z.-H. Qiao,
    Resolving Knudsen Layer by High Order Moment Expansion,
    Continuum Mechanics and Thermodynamics, 31(5), 2019, pp. 1313-1337.
    DOI:10.1007/s00161-019-00749-3

  66. R. Li, Z.-Y. Sun, F.-Y. Yang, Z.-J. Yang,
    A finite element method by patch reconstruction for the Stokes problem using mixed formulations,
    Journal of Computational and Applied Mathematics, Volume 353, June 2019, pp. 1-20.
    DOI: 10.1016/j.cam.2018.12.017

    67. 2019

  67. L. Chen, G.-H. Hu and R. Li,
    Integrated linear reconstruction for finite volume scheme on arbitrary unstructured grids,
    Communications in Computational Physics, 24 (2018), pp. 454-480.
    DOI: 10.4208/cicp.OA-2017-0137

  68. Y.-N. Di, Y.-W. Fan, Z.-Z. Kou, R. Li and Y.-L. Wang,
    Filtered hyperbolic moment method for the Vlasov Equation,
    Journal of Scientific Computing, 79, 2019, pp. 969-991.
    DOI: 10.1007/s10915-018-0882-8

  69. L. Chen, R. Li and C.-B. Yao,
    An approximate solver for multi-medium Riemann problem with Mie-Gruneisen equations of state,
    Research in Mathematical Sciences, 5(31).
    DOI: 10.1007/s40687-018-0147-z

    70. 2018

  70. 李若; 李蔚明; 宋鹏 ,
    辐射输运与电子能量强耦合源项的一种高效计算方法,
    《计算物理》卷: 34 期: 3 页: 253-260, 2017
    文献号: 1001-246X(2017)34:3<253:FSSYYD>2.0.TX;2-N

  71. Z.-C. Hu, R. Li and Z.-H. Qiao,
    Acceleration for Microflow Simulations of High-Order Moment Models by Using Lower-Order Model Correction,
    Journal of Computational Physics, Volume 327, 15 December 2016, Pages 225-244.
    DOI: 10.1016/j.jcp.2016.09.042

  72. R. Li, T. Lu and Z.-P. Sun,
    Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions,
    Frontier of Mathematics in China, 12(4), pp. 907-919, 2017.
    DOI: 10.1007/s11464-017-0612-9.

  73. Y.-N. Di, Y.-W. Fan, R. Li and L.-C. Zheng,
    Linear stability of hypebolic moment models for Boltzmann equation,
    Numerical Mathematics: Theory, Method and Application, Vol. 10, No. 2, pp. 255-277, May 2017
    DOI: 10.4208/nmtma.2017.s04

  74. Y.-N. Di, Y.-W. Fan and R. Li,
    13-Moment System with Global Hyperbolicity for Quantum Gas,
    Journal of Statistical Physics, 167, 2017, pp. 1280-1302. First Online: 31 March 2017
    DOI: 10.1007/s10955-017-1768-0


    75. 2017

  75. 蔡振宁，樊玉伟，胡志成，李若，王何宇,
    矩方法在动理 学中的发展与应用,
    《中国科学：信息科学》, 46(10), 页码： 1465-1488, 2016

    Z.-N. Cai, Y.-W. Fan, Z.-C. Hu, R. Li and H.-Y. Wang,
    The development and application of the moment method in the gas kinetic theory(in Chinese),
    SCIENTIA SINICA Informationis, 46(10), pp. 1465-1488, 2016
    DOI: 10.1360/N112016-00098

  76. 蔡振宁，樊玉伟，李若,
    从离散速度模型到矩方法 ,
    《计算数学》2016年第3期，页码：227-244

    Z.-N. Cai, Y.-W. Fan and R. Li,
    From discrete velocity model to moment method,
    Journal of Computational Mathematics (in Chinese), 2016(3), pp. 227-244.

  77. Z.-C. Hu, R. Li and Z.-H. Qiao,
    Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation,
    Communications in Computational Physics, 20(3), pp. 551-582, September, 2016.
    DOI: 10.4208/cicp.290615.020316a

  78. Y.-C. Jiang, R. Li and S.-N. Wu,
    A Second Order Time Homogenized Model for Sediment Transport,
    Multiscale Modelling and Simulation, 14(3), pp. 965-996, July, 2016.
    DOI: 10.1137/15M1041778

  79. G. Alldredge, R. Li and W.-M. Li,
    Approximating the $M_2$ Method by the Extended Quadrature Method of Moments for Radiative Transfer in Slab Geometry,
    Kinetic and Related Models, 9(2), pp. 237-249, June, 2016.
    DOI: 10.3934/krm.2016.9.237

  80. L. Chen and R. Li,
    An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids,
    Journal of Scientific Computing, pp. 1-26, 2016. First online: 11 February, 2016.
    DOI: 10.1007/s10195-016-0173-1.

  81. Y.-H. Guo, R. Li and C.-B. Yao,
    A Numerical Method on Eulerian Grids for Two-phase Compressible Flow,
    Advances in Applied Mathematics and Mechanics, 8(2), pp. 187-212, 2016.
    DOI: 10.4208/aamm.2014.m706

  82. Y.-W. Fan, J. Koellermeier, J. Li, R. Li and M. Torrilhon,
    Model Reduction of Kinetic Equations by Operator Projection,
    Journal of Statistical Physics, 162(2), pp 457-486, 2016. First online: 29 October, 2015.
    DOI: 10.1007/s10955-015-1384-9

    83. 2016

  83. 樊玉伟, 李若,
    基于广义Hermite展开的全局双曲矩方程组,
    《中国科学：数学》45卷, 页码：1635-1676.

    Y.-W. Fan and R. Li,
    Globally hyperbolic moment system by generalized Hermite expansion,
    (in Chinese). Sci Sin Math, 2015, 45: 1635-1676.
    DOI: 10.1360/012015-23

  84. Z.-N. Cai, Y.-W. Fan and R. Li,
    A Framework on Moment Model Reduction for Kinetic Equation,
    SIAM Journal on Applied Mathematics, 75(5), pp 2001-2023, 2015.
    DOI: 10.1137/14100110X

  85. Y.-N. Di, Z.-Z. Kou and R. Li,
    High Order Moment Closure for Vlasov-Maxwell Equations,
    Front. Math. China, 10(5), 2015, pp. 1087-1100.
    DOI: 10.1007/s11464-015-0463-1

    86. 2015

  86. 杨青, 李若, 蔡振宁,
    六自由度外弹道方程组的快速数值方法,
    《高校计算数学学报》，第36卷第3期，2014，页码：253-270.

  87. Z.-C. Hu and R. Li,
    A Nonlinear Multigrid Steady-State Solver for 1D Microflow,
    Computer and Fluids, 103, 2014, pp. 193-203.

  88. Z.-N. Cai, Y.-W. Fan and R. Li,
    On Hyperbolicity of 13-Moment System,
    Kinetic and Related Models, 7(3), 2014, pp. 415-432.

  89. R. Li, T. Lu and Z.-P. Sun,
    Stationary Wigner Equation with Inflow Boundary Conditions: Will a Symmetric Potential Yield a Symmetric Solution?,
    SIAM Journal on Applied Mathematics, 74(3), 2014, pp.885-897.
    DOI: 10.1137/130941754

  90. R. Li, T. Lu and W.-Q. Yao,
    Discrete Kernel Preserving Model for 1D Electron-Optical Phonon Scattering,
    Journal of Scientific Computing, February 2015, 62(2), pp 317-335.
    DOI: 10.1007/s10915-014-9858-5

  91. Z.-N. Cai and R. Li,
    The NRxx Method for Polyatomic Gases,
    Journal of Computational Physics, Available online 28 February 2014. 267(15), June 2014, pp.63-91
    DOI: 10.1016/j.jcp.2014.02.026

  92. Z.-C. Hu, R. Li, T. Lu, Y.-L. Wang and W.-Q. Yao,
    Simulation of an n+-n-n+ Diode by Using Globally-Hyperbolically-Closed High-Order Moment Models,
    Journal of Scientific Computing, 59(3), Page 761-774, 2014.
    DOI: 10.1007/s10915-013-9781-1

  93. R. Li, T. Lu, Y.-L. Wang and W.-Q. Yao,
    Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation,
    Communcations in Computational Physics, Vol. 15, pp. 569--595, 2014.
    DOI: 10.4208/cicp.091012.120813a.

  94. Z.-N. Cai, Y-W. Fan, R. Li, and Z.-H. Qiao,
    Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision,
    Communications in Computational Physics, 15(5), pp. 1368-1406, May 2014.
    DOI: 10.4208/cicp.220313.281013a.

  95. Z.-N. Cai, R. Li and Y.-L. Wang,
    Solving Vlasov Equations Using NRxx Method,
    SIAM Journal on Scientific Computing, 35(6), pp. A2807-A2831, 5 December, 2014.
    DOI: 10.1137/120871791

    96. 2014

  96. 闫凯, 李若, 田宙, 郭永辉, 曹渊,
    强爆炸火球数值模拟中的算子分裂方法,
    《计算物理》, 第30卷第3期，2013，页码：379-386.

  97. W.-Q. Yao, R. Li, T. Lu, X.-Y. Liu, G. Du and K. Zhao,
    Globally hyperbolic moment method for BTE including phonon scattering,
    The International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2013) 3-5 September, 2013, Glasgow, Scotland, UK. Pages: 300-303, Product Type: Conference Publications

  98. Z.-N. Cai, Y.-W. Fan and R. Li,
    Globally Hyperbolic Regularization of Grad's Moment System,
    Communications on Pure and Applied Mathematics, . Published as 67(3):464-518, 2014. First online at 1 July 2013
    DOI: 10.1002/cpa.21465

  99. Z.-N. Cai, R. Li and Z.-H. Qiao,
    Globally Hyperbolic Regularized Moment Method with Applications to Microflow Simulation,
    Computer and Fluids, 81, 20 July 2013, Pages 95-109.

  100. J. Deng, R. Li, T. Sun and S.-N. Wu,
    A Robust Simulation for Shallow Flows on Complex Rough Topography,
    Numerical Mathematics: Theory , Methods and Applications, 6(2), 2013, pp 384-407.

  101. Z.-N. Cai, Y.-W. Fan, R. Li, T. Lu and W.-Q. Yao,
    Quantum Hydrodynamic Model of Density Functional Theory,
    Journal of Mathematical Chemistry, Vol. 51, No. 5, pp. 1747--1771, 2013
    DOI: 10.1007/s10910-013-0176-1.

  102. R. Li and S.-N. Wu,
    $H$-adaptive Mesh Method with Double Tolerance Adaptive Strategy for Hyperbolic Conservation Laws,
    Journal of Scientific Computing, 56(3), pp. 616--636, 2013.
    DOI: 10.1007/s10915-013-9692-1

    103. 2013

  103. Z.-N. Cai, Y.-W. Fan and R. Li,
    Globally Hyperbolic Regularization of Grad's Moment System in One Dimensional Space,
    Communications in Math Sciences, 11(2), 2012, pp. 547-571.

  104. Z.-N. Cai, Y.-W. Fan, R. Li, T. Lu and Y.-L. Wang,
    Quantum Hydrodynamic Model by Moment Closure of Wigner Equation,
    Journal of Mathematical Physics, 53(10), 2012.
    DOI: 10.1063/1.4748971

  105. R. Li, P.-B. Ming and F.-Y. Tang,
    An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems,
    Multiscale Modelling and Simulation, 10(1), 2012, pp. 259-283.
    DOI: 10.1137/110836626

  106. Z.-N. Cai, R. Li and Z.-H. Qiao,
    NRxx Simulation of Microflows with Shakhov Model,
    SIAM Journal on Scientific Computing, 34(1), 2012, pp. A339-A369.
    DOI: 10.1137/110828551

  107. Z.-N. Cai, R. Li and Y.-L. Wang,
    Numerical Regularized Moment Method for High Mach Number Flow,
    Communication in Computational Physics, 11(5), 2012, pp. 1415-1438.

    108. 2012

  108. Z.-N. Cai, R. Li and Y.-L. Wang,
    An Efficient NRxx Method for Boltzmann-BGK Equation,
    Journal of Scientific Computing, 50, 2012, pp. 103-119
    DOI: 10.1007/s10915-011-9475-5.

  109. G. Yuan and R. Li,
    Sharp a Posteriori Error Estimate for Elliptic Equation with Singular Data,
    Frontiers of Mathematics in China, 6(1), 2011, pp. 177-202.

  110. G.-H. Hu, R. Li, and T. Tang,
    A robust WENO type finite volume solver for steady Euler equations on unstructured grids,
    Communications in Computational Physics, 9 (2011), pp. 627-648. journal download

    111. 2011

  111. K. Kunisch, W.-B. Liu, Y.-Z. Chang, N.-N. Yan and R. Li,
    Adaptive finite element approximation for a class of parameter estimation problems,
    Journal of Computational Mathematics (28), 01/2010, pp 645-675.

  112. Z.-N. Cai and R. Li,
    Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation,
    SIAM Journal on Scientific Computing, Volume 32, Issue 5, September 23, 2010, pp. 2875-2907.
    DOI: 10.1137/100785466

  113. D. Wang, R. Li and N.-N. Yan,
    An Edge-based Anisotropic Mesh Refinement Algorithm and its Application to Interface Problems,
    Communications in Computational Physics Volume 8 (2010), pp. 511-540 local download, journal download

  114. Z.-N. Cai and R. Li,
    An $h$-Adaptive Mesh Method for Boltzmann-BGK/Hydrodynamics Coupling,
    Journal of Computational Physics Volume 229, Issue 5, 1 March 2010, Pages 1661-1680.
    DOI: 10.1016/j.jcp.2009.10.050.

  115. G.-H. Hu, R. Li and T. Tang,
    A Robust High-order Residual Distribution Type Scheme for Steady Euler Equations on Grids,
    Journal of Computational Physics Volume 229, Issue 5, 1 March 2010, Pages 1681-1697.
    DOI: 10.1016/j.jcp.2009.11.002

    116. 2010

  116. X.-L. Hu, R. Li and T. Tang,
    A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Equations,
    Commun. Comput. Phys., 5 (2009), pp. 1012-1029. local download, Journal download.

  117. Y.-N. Di and R. Li,
    Computation of Dendritic Growth with Level Set Model Using a Multi-Mesh Adaptive Finite Element Method,
    Journal of Scientific Computing 39 (2009), pp. 441-453.
    DOI: 10.1007/s10915-009-9275-3

    118. 2009

  118. T. Y. Hou and R. Li,
    Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations,
    Mathematics and Computation, a Contemporary View, Abel Symposium 3 (2008)
    DOI: 10.1007/978-3-540-68850-1_3

  119. Y.-N. Di, R. Li and T. Tang,
    A General Moving Mesh Framework in 3D and Its Application for Simulating the Mixture of Multi-Phase Flows,
    Communications in Computational Physics 3(3), 2008, 582-602 local download, Journal download.

  120. R. Li, X. Wang and W.-B. Zhao,
    A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids,
    Numerical Mathematics: Theory, Methods and Applications 1(1), 2008, 92-112 local download, Journal download.

  121. T. Y. Hou and R. Li,
    Blowup or No Blowup? The Interplay between Theory and Numerics,
    Physics D, 37, 1937-1944, 2008.
    DOI: 10.1016/j.physd.2008.01.018

  122. H.-Y. Wang, R. Li and T. Tang,
    An Efficient $r$-adaptive Finite Element Method for Phase Field Model of Dendritic Growth,
    Journal of Computational Physics, 2008, vol 227, pp. 5984-6000.
    DOI: 10.1016/j.jcp.2008.02.016

  123. W. Gong, R. Li, N.-N. Yan and W.-B. Zhao,
    An Improved Error Analysis for Finite Element Approximation of Bioluminescence Tomography,
    Journal of Computational Mathematics 26(3), 2008, pp. 297-309 local download, Journal download.

  124. H.-Y. Wang and R. Li,
    Mesh Sensitivity for Numerical Solutions of Phase-field Equations Using r-adaptive Finite Element Methods,
    Communications in Computational Physics 3(2), 2008, 357-375 local download, Journal download.

    125. 2008

  125. R. Li, W.-B. Liu and N.-N. Yan,
    A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems,
    Journal of Scientific Computing 33(2), November 2007, 155-182 doi:10.1007/s10915-007-9147-7.

  126. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang,
    Level Set Calculations for Incompressible Two-phase Flows on a Dynamically Adaptive Grid,
    Journal of Scientific Computing, 31(2007), 1-2, pp75-98, doi:10.1007/s10915-006-9119-3.

  127. T. Y. Hou and R. Li,
    Computing Nearly Singular Solutions Using Pseudo-Spectral Methods,
    Journal of Computational Physics, 226 , 379-397, 2007 doi:10.1016/j.jcp.2007.04.014.

  128. D.-M. Li, R. Li and P.-W. Zhang,
    A Cellular Automaton Technique for Modelling of a Binary Dendritic Growth with Convection,
    Applied Mathematical Modelling, 31(2007), pp 971-982. doi:10.1016/j.apm.2006.04.004.

  129. T. Y. Hou and R. Li,
    Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations,
    Discrete and Continuous Dynamical Systems, Series A , 18(4) , 637-642, 2007, Journal download.

  130. Y.-Q. Huang, R. Li and W.-B. Liu,
    Preconditioned Descending Algorithms for $p$-Laplacian,
    Journal of Scientific Computing 32(2), 2007, 342-371 doi:10.1007/s10915-007-9134-z.

    131. 2007

  131. D.-M. Li, R. Li, P.-W. Zhang,
    A Cellular Automaton Technique for the Modeling of Solidification Microstructure in Multi-Component Alloys,
    Computer and Computational Sciences, 2006. IMSCCS '06. First International Multi-Symposiums on; 07/2006.

  132. R. Li and T. Tang,
    Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws,
    Journal of Scientific Computing, 27, 2006, pp.347-363, doi:10.1007/s10915-005-9045-9

  133. J. Deng, T. Y. Hou, R. Li and X.-W. Yu,
    Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation,
    Methods and Applications of Analysis 13(2), 2006, 157-180 Journal download.

  134. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang,
    Moving Mesh Methods for Singular Problems on a Sphere Using Perturbed Harmonic Mappings,
    SIAM Journal on Scientific Computing, 28(2006), pp1490-1508, doi:10.1137/050642514.

  135. T. Y. Hou and R. Li,
    Dynamic Depletion of Vortex Stretching and Non-blowup of the 3D Incompressible Euler Equations,
    Journal of Nonlinear Science, 16(6), 639-664, 2006. doi:10.1007/s00332-006-0800-3.

  136. D.-M. Li, R. Li, P.-W. Zhang,
    A Cellular Automaton Technique for the Modeling of Solidification Microstructure in Multi-component Alloys,
    First International Multi-Symposiums on Computer and Computational Sciences (IMSCCS 2006), Proceedings, Vol 2, 2006, pp 800-806 doi:10.1109/IMSCCS.2006.142

    137. 2006

  137. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang,
    Moving Mesh Finite Element Methods for the Incompressible Navier-Stokes Equations,
    SIAM Journal on Scientific Computing, 26 (2005), 1036-1056, doi:10.1137/030600643.

  138. R. Li,
    on Multi-Mesh $h$-Adaptive Algorithm,
    Journal of Scientific Computing 24(3), 2005, pp.321-341, doi:10.1007/s10915-004-4793-5.

    139. 2005

  139. D.-M. Li, R. Li and P.-W. Zhang,
    A New Coupled Model for Alloy Solidification,
    Science in China Series A-Mathematics 47: 41-52 Suppl. S Apr 2004, Journal download.

  140. R. Li, C. Luo and P.-W. Zhang,
    Numerical Simulation of Doi Model of Polymeric Fluids,
    Adv. in Sci. Comput. & Appl. (Y. Lu, W. Sun and T. Tang eds), 2004, pp 258-273. doi:10.1.1.110.7638

    141. 2004

  141. R. Li, W.-B. Liu and H.-P. Ma,
    Moving Mesh Finite Element Approximations for Variational Inequality I: Static Obstacle Problem,
    Journal of Scientific Computing, 21(1), pp. 31-55 (2003), doi:10.1023/B:JOMP.0000027954.83289.00.

    142. 2003

  142. R. Li, T. Tang and P.-W. Zhang,
    A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions,
    Journal of Computational Physics 177, 365-393 (2002), doi:10.1006/jcph.2002.7002.

  143. R. Li, W.-B. Liu, H.-P. Ma and T. Tang,
    Adaptive Finite Element Approximations for Distributed Optimal Control Problems,
    SIAM Journal on Control and Optimization, 41 : pp. 1321-1349 (2002), doi:10.1137/S0363012901389342.

    144. 2002

  144. R. Li, T. Tang and P.-W. Zhang,
    Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps,
    Journal of Computational Physics 170, 562-588 (2001), doi:10.1006/jcph.2001.6749.

  145. R. Li, W.-B. Liu, T. Tang and P.-W. Zhang,
    Moving Mesh Finite Element Methods Based on Harmonic Maps,
    Proc. of 2nd Intl. Workshop on Sci. Comput. and Appl. (P. Minev and Y. Lin eds), 2001, pp. 143-156, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.32.435&rep=rep1&type=pdf.

  146. Q. Du, D.-Z. Li, Y.-Y. Li, R. Li and P.-W. Zhang,
    Simulating a Double Casting Technique Using Level Set Method,
    Computational Materials Science, 22, 200-212, 2001.
    DOI: 10.1016/S0927-0256(01)00190-2

    147. 2001

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