Books, Special Issues, and Proceedings

    1. The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, SIAM Frontiers in Applied Mathematics 33, 2006, ISBN-10: 0-89871-609-8 / ISBN-13: 978-0-898716-09-2, Zhilin Li and Kazufumi Ito.  Erratum.
    2. Z. Li, Z. Qiao, T. Tang, Numerical Solution of Differential Equations -- Introduction to Finite Difference and Finite Element Methods, Cambridge University Press, 2017, ISBN: 978-1-107-16322-5.
    3. An Introduction to Partial Differential Equations,  Zhilin Li and Larry Norris, World Scientific Publisher
    4. Layton, A., Stockie, J., Li, Z. L., and Huang, H. X. (2012). Special issue on fluid motion driven by immersed structures preface. Communications in Computational Physics, 12(2), I-III.
    5. T. Witelski, D. Ambrose, A. Bertozzi, A. Layton, Z. Li, M. Minion, Special Issue of  Discrete and continuous dynamical systems. Series B, 2012; 17(4).  Fluid dynamics, Analysis, and Numerics (FAN), A conference in honor of  J. Thomas Beale,
    6. Moving Interface Problems and Application in Fluid Dynamics, AMS Contemporary Mathematics, Vol. 466, 2008, B-C. Khoo, Z. Li, and P. Ling, Editors.
    7. Special issue of Applied Numerical Mathematics for the International Conference on Scientific Computing, Nanjing, China, June 4 -- June 8, 2005, Vol. 57, issues 5-7, 2007, Z. Li, Y. Song, and T. Tang editors.
    8. Interface Problems and Methods in Biological and Physical Flows, Lecture Notes Series,  Vol. 17, IMS, Singapore, World Scientific, 2008, B-C. Khoo, Z. Li, and P. Ling, Editors.
    9. Numerical Analysis and Applications, Lecure Notes in Computer Sciences, LNCS 3401, Springer, 2005, Z. Li, L. Vulkov, J. Wasniewski, Editors.
    10. Industrial Mathematics, SIAM Publisher, Philadelphia,  ISBN O-89871-467-2, 2000,  P. Gremaud, Z. Li, R. Smith, and H. Tran.

Publications

Errtum of some papers.




Book Chapter:
  1. Immersed Interface/Boundary Method, K. Ito and Z. Li, in Encyclopedia of Applied and Computational Mathematics, editor, Springer-Verlag Berlin Heidelberg 2015 Björn Engquist, 10.1007/978-3-540-70529-1_387

SIAM Book Review:
  1. Introduction to Scientific Computing and Data Analysis (Mark H. Holmes), SIAM Review, Vol. 59, No.3, 689-690, 2017.
  2. Generalized Difference Methods for Differential Equations. By R. Li, Z. Chen, and W. Wu. Marcel Dekker, N,  SIAM Review, Vol. 43, No.1, 203-205, 2001.


 Selected Publications:

  1. A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes COMPUTERS & FLUIDS, 269. S. Chai, Z. Li , Z. Zhang, Z. Zhang
  2. Coupled transformation methods and analysis for BVPs on infinite domains Li, Z., & Pan, K. (2024, July). JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol. 444. Z. Li & K. Pan 
  3. Fully accurate approximation of piecewise smooth functions using corrected B-spline quasi-interpolants COMPUTATIONAL & APPLIED MATHEMATICS, 43(4). Z. Li n , K. Pan , J. Ruiz  & D. Yanez 
  4. High order compact augmented methods for Stokes equations with different boundary conditions Computer Physics Communications. K. Pan, J. Li & Z. Li
  5. New third-order convex splitting methods and analysis for the phase field crystal equation Ye, Z., Zheng, Z., & Li, Z. (2024, February 28). NUMERICAL ALGORITHMS, Vol. 2. By: Z. Ye , Z. Zheng  & Z. Li
  6. A CELL-CENTERED MULTIGRID SOLVER FOR THE FINITE VOLUME DISCRETIZATION OF ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS ON IRREGULAR DOMAINS. JOURNAL OF COMPUTATIONAL MATHEMATICS, Vol. 12. By: K. Pan, X. Wu, H. Hu & Z. Li
  7. A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, Vol. 7. By: B. Dong*, Z. Li n  & J. Ruiz-Alvarez 
  8. Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods APPLIED MATHEMATICS AND COMPUTATION, 459. By: J. Li *, Z. Li n  & K. Pan
  9. Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms JOURNAL OF SCIENTIFIC COMPUTING, 95(3). By: S. Amat , Z. Li n , J. Ruiz-Alvarez , C. Solano  & J. Trillo
  10. An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 403. By: S. Hu , K. Pan, X. Wu, Y. Ge & Z. Li
  11. Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 57(4), 2041–2076. By: H. Ji, F. Wang, J. Chen & Z. Li
  12. HIGH ORDER COMPACT SCHEMES FOR FLUX TYPE BCS SIAM JOURNAL ON SCIENTIFIC COMPUTING, 45(2), A646–A674. By: Z. Li n  & K. Pan
  13. Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems Research Reports on Computer Science, 2(1), 15–27. By: B. Dong, Z. Li  & J. Ruiz-Álvarez
  14. New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 16(2), 393–409. By: K. Pan, K. Fu, J. Li, H. Hu & Z. Li
  15. Numerical analysis of a free boundary problem with non-local obstacles APPLIED MATHEMATICS LETTERS, 135. By: Z. Li n  & H. Mikayelyan
  16. Numerical integration rules with improved accuracy close to discontinuities MATHEMATICS AND COMPUTERS IN SIMULATION, 210, 593–614. By: S. Amat , Z. Li n , J. Ruiz-Alvarez , C. Solano  & J. Trillo
  17. Stable high order FD methods for interface and internal layer problems based on non-matching grids Li. NUMERICAL ALGORITHMS, Vol. 11. By: Z. Li n , K. Pan & J. Ruiz-Alvarez
  18. A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, Vol. 2. By: R. Li, J. Yin & Z. Li
  19. A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 449. By: K. Pan , X. Wu, H. Hu , Y. Yu  & Z. Li
  20. A new parameter free partially penalized immersed finite element and the optimal convergence analysis NUMERISCHE MATHEMATIK, 150(4), 1035–1086. By: H. Ji, F. Wang, J. Chen & Z. Li
  21. A new patch up technique for elliptic partial differential equation with irregularities JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 407. By: S. Singh, S. Singh & Z. Li
  22. AN L^2 SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS JOURNAL OF COMPUTATIONAL MATHEMATICS, 40(6), 2022, 882–912. By: B. Dong, X. Feng  & Z. Li
  23. An immersed C R-P-0 element for Stokes interface problems and the optimal convergence analysis COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 399. By: H. Ji , F. Wang , J. Chen & Z. Li
  24. A High Order Compact FD Framework for Elliptic BVPs Involving Singular Sources, Interfaces, and Irregular Domains JOURNAL OF SCIENTIFIC COMPUTING, 2021, 88(3). By: K. Pan , D. He & Z. Li
  25. A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices. (2021, June 3). NUMERICAL ALGORITHMS, Vol. 6. By: R. Li , Z. Li & J. Yin
  26. Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 14(3), 2021, 773–796. By: C. Zhang, Z. Li  & X. Yue

1.     S. Deng, Z. Li, K. Pan (2021), An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2021.110356

2.     B. Dong, X. Feng, & Z. Li* (2020), An FE-FD Method for Anisotropic Elliptic Interface Problems, SIAM SISC, 42(4), B1041–B1066.

3.     Tong, F., Wang, W., Feng, X., Zhao, J., & Li, Z*. (2020). How to obtain an accurate gradient for interface problems? Journal of Computational Physics, 405, 109070. https://doi.org/10.1016/j.jcp.2019.109070

4.     H. Jiang, Z. Yang & Z. Li, Non-parallel hyperplanes ordinal regression machine KNOWLEDGE-BASED SYSTEMS, 216, 106593, 2021.

5.     P. Huang & Z. Li, Partially penalized IFE methods and convergence analysis for elasticity interface problems, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 382. 10.1016/j.cam.2020.113059,2021

6.     J. Ye, Z. Yang & Z. Li, Quadratic hyper-surface kernel-free least squares support vector regression, INTELLIGENT DATA ANALYSIS, 25(2), 265–281, 2021

7.     C. Zhang, Z. Li, X. Yue, An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems, Numer. Math. Theor. Meth. Appl. doi: 10.4208/nmtma.

8.     X. Xiao, X. Feng & Z. Li, A gradient recovery-based adaptive finite element method for convection-diffusion-reaction equations on surfaces,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, DOI: 10.1002/nme.6163

9.     Z. Li, M. Lai, X. Peng & Z. Zhang, A least squares augmented immersed interface method for solving Navier–Stokes and Darcy coupling equations, Computers & Fluids, 167, 384–399, 2018.

10.  Z. Li, B. Dong, F. Tong & W. Wang, An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 119(1), 63–72.

11.  R. Hu & Z. Li, Error analysis of the immersed interface method for Stokes equations with an interface, Applied Mathematics Letters, 83, 207–211, 2018.

12.  Z. Li, X. Chen & Z. Zhang, ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT, MULTISCALE MODELING & SIMULATION, 16(4), 1623–1647, 2018.

13.  Y. Yao, Y. Zhang, L. Tian, N. Zhou, Z. Li & M. Wang, Analysis of Network Structure of Urban Bike-Sharing System: A Case Study Based on Real-Time Data of a Public Bicycle System SUSTAINABILITY, 11(19).

14.  T. Zhao, J. Zhang, Z. Li & Z. Zhang, Numerical Validations of the Tangent Linear Model for the Lorenz Equations CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 120(1), 83–104.

15.  Y. Yao, X. Jiang & Z. Li, Spatiotemporal characteristics of green travel: A classification study on a public bicycle system JOURNAL OF CLEANER PRODUCTION, 238

16.  Li, Z. L., Ji, H. F., & Chen, X. H. (2017). Accurate solution and gradient computation for elliptic interface problems with variable coefficients. SIAM Journal on Numerical Analysis, 55(2), 570-597.

17.  Huang, P. Q., & Li, Z. L. (2017). A uniformly stable nonconforming FEM based on weighted interior penalties for Darcy-Stokes-Brinkman equations. Numerical Mathematics: Theory, Methods and Applications, 10(1), 22-43.

18.  Yan, J. L., Lai, M. C., Li, Z. L., & Zhang, Z. Y. (2017). New conservative finite volume element schemes for the modified regularized long wave equation. Advances in Applied Mathematics & Mechanics, 9(2), 250-271.

19.  Qin, F. F., Chen, J. R., Li, Z. L., & Cai, M. C. (2017). A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. Computers & Mathematics with Applications, 73(3), 404-418.

20.  Li, Z. L., & Mikayelyan, H. (2016). Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer. Interfaces and Free Boundaries,18(1), 75-90.

21.  Ji, H. F., Chen, J. R., & Li, Z. L. (2016). Augmented immersed finite element methods for some elliptic partial differential equations. International Journal of Computer Mathematics, 93(3), 540-558.

22.  Zhang, S. D. M., & Li, Z. L. (2016). An augmented IIM for Helmholtz/Poisson equations on irregular domains in complex space. International Journal of Numerical Analysis and Modeling, 13(1), 166-178.

23.  Melnyk, L. J., Wang, Z. H., Li, Z. L., & Xue, J. P. (2016). Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model. Food and Chemical Toxicology, 96, 167-173.

24.  Zhang, Q., Li, Z. L., & Zhang, Z. Y. (2016). A sparse grid stochastic collocation method for elliptic interface problems with random input. Journal of Scientific Computing, 67(1), 262-280.

25.  Zhu, L., Zhang, Z. Y., & Li, Z. L. (2016). The immersed finite volume element method for some interface problems with nonhomogeneous jump conditions. International Journal of Numerical Analysis and Modeling, 13(3), 368-382.

26.  Li, Z. L. (2016). An augmented Cartesian grid method for Stokes-Darcy fluid-structure interactions. International Journal for Numerical Methods in Engineering, 106(7), 556-575.

27.  Su, X. L., Feng, X. F., & Li, Z. L. (2016). Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates. Journal of Computational Mathematics, 34(5), 499-510.

28.  Ji, H. F., Chen, J. R., & Li, Z. L. (2016). A new augmented immersed finite element method without using SVD interpolations. Numerical Algorithms, 71(2), 395-416.

29.  Zhang, Q., Ito, K., Li, Z. L., & Zhang, Z. Y. (2015). Immersed finite elements for optimal control problems of elliptic PDEs with interfaces. Journal of Computational Physics, 298, 305-319.

30.  Li, Z. L., Xiao, L., Cai, Q., Zhao, H. K., & Luo, R. (2015). A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions. Journal of Computational Physics, 297, 182-193.

31.  Zhu, L., Zhang, Z. Y., & Li, Z. L. (2015). An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions. Computers & Mathematics with Applications, 70(2), 89-103.

32.  Alvarez, J. R., & Li, Z. L. (2015). The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow. Applied Mathematics and Computation, 264, 179-197.

33.  On convergence of the immersed boundary method for elliptic interface problems, Zhilin Li,  Math. of Comp., in press, Published electronically: December 16, 2014, http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2014-02932-3/home.html

34.  Xia, J. L., Li, Z. L., & Ye, X. (2015). Effective matrix-free preconditioning for the augmented immersed interface method. Journal of Computational Physics, 303, 295-312.

35.  Zeng, Y. P., Chen, J. R., & Li, Z. L. (2015). A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems. International Journal of Computer Mathematics, 92(2), 394-410.

36.  H. Ji, J. Chen, Z. Li, A symmetric and consistent immersed finite element method for interface problems, Journal of Scientific Computing, Volume 61, Number 3, December 2014, pp.533-557.

37.  Xu, J. J., Huang, Y. Q., Lai, M. C., and Li, Z. L. (2014). A coupled immersed interface and level set method for three-dimensional interfacial flows with insoluble surfactant. Communications in Computational Physics, 15(2), 451-469.

38.  Li, Z. L., Wang, L., Aspinwall, E., Cooper, R., Kuberry, P., Sanders, A., & Zeng, K. (2015). Some new analysis results for a class of interface problems. Mathematical Methods in the Applied Sciences, 38(18), 4530-4539.

39.  Liu, X. P., Wang, C. H., Wang, J., Li, Z. L., Zhao, H. K., and Luo, R. (2013). Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications. Physical Chemistry Chemical Physics, 15(1), 129-141.

40.  Botello-Smith, W. M., Liu, X. P., Cai, Q., Li, Z. L., Zhao, H. K., and Luo, R. (2013). Numerical Poisson-Boltzmann model for continuum membrane systems. Chemical Physics Letters, 555, 274-281.

41.  Z. Wang, Z. Li, S. Lubkin, A Robin-Robin Domain Decomposition Method for a Stokes-Darcy Structure Interaction with a Locally Modified Mesh,  Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 435-446.

42.  Song, P., Xue, J. P., and Li, Z. L. (2013). Simulation of longitudinal exposure data with variance-covariance structures based on mixed models. Risk Analysis, 33(3), 469-479.

43.  Wang, Q. X., Zhang, Z. Y., and Li, Z. L. (2013). A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere. Applied Numerical Mathematics, 71, 1-13.

44.  Li, Z. L., and Song, P. (2013). Adaptive mesh refinement techniques for the immersed interface method applied to flow problems. Computers and Structures, 122, 249-258.

45.  Wang, C. H., Wang, J., Cai, Q., Li, Z. L., Zhao, H. K., and Luo, R. (2013). Exploring accurate Poisson-Boltzmann methods for biomolecular simulations. Computational and theoretical chemistry, 1024, 34-44.

46.  Li, Z. L., and Song, P. (2012). An adaptive mesh refinement strategy for immersed boundary/interface methods. Communications in Computational Physics, 12(2), 515-527.

47.  Hou, S. M., Li, Z. L., Wang, L. Q., and Wang, W. (2012). A numerical method for solving elasticity equations with interfaces. Communications in Computational Physics, 12(2), 595-612.

48.  Ito, K., Li, Z. L., and Qiao, Z. H. (2012). The sensitivity analysis for the flow past obstacles problem with respect to the Reynolds number. Advances in Applied Mathematics and Mechanics, 4(1), 21-35.

49.  Wan, X. H., and Li, Z. L. (2012). Some new finite difference methods for Helmholtz equations on irregular domains or with interfaces. Discrete and Continuous Dynamical Systems-Series B, 17(4), 1155-1174.

50.  Caraus, I., and Li, Z. L. (2012). Numerical solutions of the system of singular integro-differential equations in classical holder spaces. Advances in Applied Mathematics and Mechanics, 4(6), 737-750.

51.  Ho, J., Li, Z. L., and Lubkin, S. R. (2012). An augmented immersed interface method for moving structures with mass. Discrete and Continuous Dynamical Systems-Series B, 17(4), 1175-1184.

52.  Alvarez, J. A., Chen, J. R., and Li, Z. L. (2011). The IIM in polar coordinates and its application to electro capacitance tomography problems. Numerical Algorithms, 57(3), 405-423.

53.  Xie, H., Li, Z. L., and Qiao, Z. H. (2011). A finite element method for elasticity interface problems with locally modified triangulations. International Journal of Numerical Analysis and Modeling, 8(2), 189-200.

54.  Wu, C. T., Li, Z. L., and Lai, M. C. (2011). Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method. International Journal of Numerical Analysis and Modeling, 8(3), 466-483.

55.  Xu, J. J., Li, Z. L., Lowengrub, J., and Zhao, H. K. (2011). Numerical study of surfactant-laden drop-drop interactions. Communications in Computational Physics, 10(2), 453-473.

56.  Feng, X. F., Li, Z. L., and Qiao, Z. H. (2011). High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients. Journal of Computational Mathematics, 29(3), 324-340.

57.  Li, Z. L., Lai, M. C., He, G. W., and Zhao, H. K. (2010). An augmented method for free boundary problems with moving contact lines. Computers and Fluids, 39(6), 1033-1040.

58.  Gong, Y., and Li, Z. L. (2010). Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions. Numerical Mathematics: Theory, Methods and Applications, 3(1), 23-39.

59.  The sensitivity analysis for the flow past obstacles problem with respect to the Reynolds number, K. Ito, Z. Li, and Z. Qiao, Advances in Applied Mathematics and Mechanics, in press, 2011.

60.  Analysis and numerical methods for some crack problems, International Journal of Numerical Analysis & Modeling, Series B,  Vol. 2, 155-166, 2011, X.  Feng, Z. Li, and L. Wang.

61.  New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows, East Asian Journal of Applied Mathematics Vol. 1, No. 2, pp. 155-171, Zhilin Li and Ming-Chih Lai

62.  A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains, J. Comput. Phys. 228, (2009), 2616-2628, doi:10.1016/j.jcp.2008.12.028, K. Ito, M. Lai, and Zhilin Li .

63.  Numerical Study of Surfactant-Laden Drop-Drop Interactions, CiCP, Vol. 10, 2011, No. 2, pp. 453-473,  doi: 10.4208/cicp.090310.020610a,  J. Xu, Z.  Li,  J. Lowengrub, and H.  Zhao.

64.  A finite element method for elasticity interface problems with locally modified triangulations,  International Journal of Numerical Analysis & Modeling, Volume 8, Number 2, Pages 189–200, 2010, H. Xie, Z. Li,  and Z. Qiao

65.  An additive Schwartz preconditioner for the mortar-type rotated Q1 FEM for elliptic problems with discontinuous coefficients, Applied Numerical Mathematics, Vol 59, Issue 7,  2009, Pages 1657-1667, F. Wang, J. Chen, W. Xu, Z. Li.

66.  Achieving energy conservation in Poisson Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms, Chemical Physics Letters, Volume 468, Issues 4-6, 22 January 2009, Pages 112-118, Jun Wang, Qin Cai, Zhilin Li, Hong-Kai Zhao,  and Ray Luo.

67.  Correction to: "A comparison of the extended finite element method with the immersed interface method ..."[CAMCoS 1 (2006), 207--228], T. Beale, D. Chopp, R. LeVeque, and Z. Li, Comm. App. Math. Comp. Sci., Vol. 3, 95-100, 2008.

68.  Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Non-homogeneous Jump Conditions, SIAM J. Numer. Anal., Vol. 46, 472-495, 2008, Y. Gong, B. Li, and Z. Li

69.  Introduction to Immersed Boundary/Interface Method,  Robert Dillion and Zhilin Li,  Lecture Notes Series, Vol. 17, 2009, World Scientific Publisher, ISBN-13-981-283-784-1.

70.  Interface Problems and Methods in Biological Flows, B-C. Khoo, Z. Li, and P. Lin, IMS Lecture Notes Series, Vol. 17, 2009, World Scientific Publisher

71.  A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, J. Comput. Phys. Vol. 228, 2009, Pages 7821-7836, X. Yang, X. Zhang, Z. Li, and G. He

72.  An Implicit-forcing Immersed Interface Method for the Incompressible Navier-Stokes Equations, AMS Contemporary Mathematics, Vol. 466, 2008, 73-94, D-V. Le, B-C. Khoo, Z. Li

73.  An Immersed Interface Method for Solving Incompressible Viscous Flows with Piecewise Constant Viscosity Across a Moving Elastic Membrane, J. of Comput. Physics, Vol. 227 Issue 23, p9955-9983, 2008,  Z. Tan, D. V. Le, Z. Li, K. M. Lim, and B. C. Khoo

74.  Mechanics of mesenchymal contribution to clefting force in branching morphogenesis, Biomechanics and Modeling in Mechanobiology, Vol. 7, 417-426, 2008,  X. Wan, Z. Li, and S. Lubkin.

75.  An augmented approach for Stokes equations with a discontinuous viscosity and singular forces, Computers and Fluids, Vol. 36, 622-635, 2007, K. Ito, M-C. Lai, and Z. Li

76.  Pressure Jump Conditions for Stokes Equations with Discontinuous Viscosity in 2D and 3D, Methods and Applications of Analysis, Vol. 13, 199-214, 2006, K. Ito,  Z. Li, and X. Wan.

77.  A fast finite difference method for biharmonic equations on  irregular domains, Advances in Comput. Math., on-line, DOI 10.1007/s10444-007-9043-6, Vol. 29, 113-133, 2008, G. Chen, Z. Li, and P. Lin.

78.  Theoretical & numerical analysis for a fluid mixure model of tissue deformation, Q. Jiang, Z. Li, and S. Lubkin., Comm. in Comput. Phy.  Vol. 3, 620-634, 2009.

79.  A finite element method for interface problems with locally modified triangulations, AMS Contemporary Mathematics, Vol. 466, 2008, 179-190, H. Xie, K. Ito, Z. Li, J. Toivanen

80.  A study of numerical methods for the level set approach, Appl.  Numer. Math., 837-846, 2006, P. Gremaud, C. Kuster, and Z. Li

81.  An Explicit Jump Immersed Interface Method for Two-Phase Navier Stokes Equations with Interfaces, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2317-2328, 2008, with V. Rutka.

82.  An augmented IIM-level set method for Stokes equations with discontinuous viscosity,  Electron. J. Diff. Eqns., 193-210,2007

83.  A level-set method for interfacial flows with surfactant,  J. of Comput. Physics,  Vol. 212,  590-616, 2006, with  Jian-Jun Xu, John Lowengrub, and Hongkai Zhao.

84.  Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain, Journal of Computational and Applied Mathematics, Volume 191, Issue 1, 15 June 2006, Pages 106–125, Ming-Chih Lai, Zhilin Li, Xiaobiao Lin.

85.  A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES, Journal of Computational Mathematics, Vol.24, No.3, 2006, 252–264. Z. Qiao, Z. Li, T. Tang

86.  An augmented approach for the pressure boundary condition in a Stokes flow,  Comm.  in Comp. Physics, Vol. 1, (2006), pp. 874-885., Z. Li, X. Wan, K. Ito and S. R. Lubkin

87.  A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations,  Journal of Scientific Computing, 1573-7691 (Online) DOI: 10.1007/s10915-005-9019-y, With C.V. Pao and Z. Qiao.

88.  Immersed finite element for elasticity system with discontinuities,  AMS  Contemporary Mathematics, Vol. 383, pp285-298,  2005, Z. Li and X.Yang.

89.  Augmented Strategies for Interface and Irregular Domain Problems,  in Lecture Notes in Mathematics and Computer Sciences, Springer-Verlag, pp. 66-79, 2005.

90.  The numerical solution of singular integro-differential equations by reduction method using the Faber-Laurent polynomials, Iurie Caraus,  Zhilin Li, and V. A. Zolotarevskii, Differential Equations, Vol. 40, No. 12, 2004, pp. 1764-1769.

91.  Interface conditions for stokes equations with discontinuous viscosity and surface sources,  Applied Mathematics Letters ,  Vol. 19, Issue 3,  March 2006, Pages 229-234.

92.  Numerical Analysis and Its Applications, Edited by  Zhilin Li, Lubin Vulkov,  and Jerzy Was'niewski, Lecture Notes in Computer Science,  Springer-Verlag, GmbH, Volume 3401 / 2005, ISBN  3-540-24937-0.

93.  An immersed finite element space and its approximation capability, Numerical Methods of PDEs, Vol. 20,  pp.  338-367, 2004, DOI 10.1002/num.10092, Z. Li. T. Lin, Y. Lin and R. C. Rogers.

94.  Error estimates of an immersed finite element method for interface problems, NCSU CRSC Technical report, CRSC-TR00-07.

95.  Generalized Snell's law for weighted minimal surface, Methods and Applications of Analysis Vol. 10, pp. 199-214, 2003, Z. Li ,  X. Lin, M. Torres,  and H. Zhao.

96.  Three dimensional elliptic solvers for interface problems and applications, J. of Comput. Physics, Vol. 184,  pp. 215-243, 2003, with S. Deng and K. Ito, 2003.

97.  The Immersed Interface Method for Elasticity Problems with Interface, Dynamics of Continuous, Discrete and Impulsive Systems, Part A,  Vol.10, No.5, 783-808 , 2003, with X. Yang and B. Li.

98.  Solving a Nonlinear Interface Problems in Magneto-Rheological Fluids using the Immersed Interface Method.  Journal of Scientific Computing,  Vol. 19, pp. 253-266, 2003,  with K. Ito.

99.  An overview of the immersed interface method and its applications, Taiwanese J. Mathematics, Vol. 7, No. 1, pp. 1-49, 2003.

100.  AN L ∞ SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS, B. Dong, X. Feng, & Z. Li* (2020), J. Comput. Math., 2021

101.  Introduction to Partial Differential Equations,  Z. Li & L. Norris, World Scientific, https://dx.doi.org/10.1142/12052, 2021

102.       Force and Deformation on Branching Rudiments: Cleaving Between Hypotheses, Biomechanics and Modeling in mechanobiology, Vol. 1,  pp. 5-16, 2002, with Sharon Lubkin.

103.       A fast finite difference method for solving Navier-Stokes Equations on irregular domains, J. of Commu. in Math.  Sci., Vol. 1,  pp. 180-196, 2003. with C. Wang.

104.       The Level-Set Function Approach to an Inverse Interface Problem, Inverse Problems,  Vol. 17, No. 5, October, 2001, pp. 1225-1242, with K. Ito and K. Kunish.

105.       Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients, SIAM J. Sci. Comput. 23, No.1, pp. 339-361,  2001, with K. Ito

106.       Immersed Interface Method for the Navier-Stokes Equations with Singular Forces,  J. of Comput. Physics,  171, 822-842 (2001), with M. Lai.

107.       Numerical Analysis of Interfacial 2D Stokes Flow with Discontinuous Viscosity and Variable Surface Tension,  Numerical Methods in Fluids, 37, 525-540, 2001, with S. Lubkin.

108.       A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane, Applied Math. Letters, 14, pp. 149-154, 2001 with M. Lai.

109.       A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals, in Numerical Analysis and Its Application, edited by L. Vulkov, J. Wasniewski, and P. Yalamov, Springer-Verlag, pp. 527-534, 2001, with W. Cai

110.       Numerical method for simulation of bubbles flowing through another fluid, in Advances in Scientific Computing, edited by Z-C Shi et. el., Science Press, pp. 86-94, 2001, with Y. Shen.

111.       A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid,  J. of Comput. Physics,  152:281-304, 1999, with H. Zhao and H Gao.

112.       New Cartesian grid methods for interface problems using the finite element formulation, Numerische Mathematik,  96:61-98, 2003,  also, NCSU CRSC-TR99-5, 1999, with T. Lin,  and X. Wu.

113.       A numerical method for solving heat equations involving interfaces, Electron. J. Diff. Eqns., Conf. 03, 1999, pp. 100-108, with Y. Shen.

114.       The immersed finite volume element methods for the elliptic interface problems, Mathematics and Computers In Simulation, (50)1-4 (1999) pp. 43-61, with R.  E. Ewing, T. Lin,  and Y. Lin

115.       A fast iterative algorithm for elliptic interface problems.  SIAM J. Numer. Anal.  35:230--254, 1998.

116.       The immersed interface method using a finite element formulation. Applied Numer. Math.  27:253--267, 1998.

117.      Convergence analysis of the immersed interface method.  IMA J. Numer. Anal., 19:583-608, 1999, with H. Hunag.

118.      Fast and Accurate Numerical Approaches for Stefan Problems and Crystal Growth. Numerical Heat Transfer,  Part B: Fundamentals,35: 461-484, 1999, with B. Soni

119.      Theoretical and numerical analysis on a thermo-elastic system with discontinuities. J. of Comput. Appl. Math. 91:1--22, 1998, with J. Zou.

120.      An Inverse Problem in a Parabolic Equation, Electronic Journal of Differential Equations, Conference 01, 1997, pp. 193--199, Published November 12, 1998, with K. Zheng.

121.      Crack jump conditions for elliptic problems, Applied Math. Letters,12(6):81--88, 1999, with A. Wiegmann and R. LeVeque

122.      A hybrid method for moving interface problems with application to the Hele-shaw flow, J. Comput. Phys. 134:236--252, 1997, with T. Hou, S. Osher, and H.

123.      A numerical method for diffusive transport with moving boundaries and discontinuous material properties. International J. Numer. & Anal. Method in Geomechanics, 21:653--662, 1997, with D. McTigue, and J. Heine.

124.      Convergence analysis of the immersed interface method.  IMA J. Numer. Anal., 19:583-608, 1999, with H. Hunag.

125.      Fast and Accurate Numerical Approaches for Stefan Problems and Crystal Growth. Numerical Heat Transfer,  Part B: Fundamentals,35: 461-484, 1999, with B. Soni

126.      Theoretical and numerical analysis on a thermo-elastic system with discontinuities. J. of Comput. Appl. Math. 91:1--22, 1998, with J. Zou.

127.      An Inverse Problem in a Parabolic Equation, Electronic Journal of Differential Equations, Conference 01, 1997, pp. 193--199, Published November 12, 1998, with K. Zheng.

128.      Crack jump conditions for elliptic problems, Applied Math. Letters,12(6):81--88, 1999, with A. Wiegmann and R. LeVeque

129.      A hybrid method for moving interface problems with application to the Hele-shaw flow, J. Comput. Phys. 134:236--252, 1997, with T. Hou, S. Osher, and H.

130.       Immersed interface method for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18:709--735, 1997, with  R. J. LeVeque.


131.       Immersed interface method for moving interface problems.  Numerical Algorithms, 14:269-293, 1997

132.       A note on immersed interface methods for three-dimensional elliptic equations. Computers Math. Appl.  31:9--17, 1996.


133.       Simulation of bubbles in creeping flow using the immersed interface method, in Proc. Sixth International Symposium on Computational Fluid,  pp 688-693, 1995,  with  R. J. LeVeque

134.       The Immersed Interface Method --- A Numerical Approach for Partial Differential Equations with Interfaces, PhD thesis, University of Washington, 1994.

135.       The immersed interface method for elliptic equations with discontinuous coefficients and singular sources,  SIAM J. Numer. Anal. 31:1019--1044, 1994, with  R. J. LeVeque

136.       Erratum: "The immersed interface method for elliptic equations with discontinuous coefficients and singular sources",  SIAM J. Numer. Anal. 32:1704, 1995, with

137.       ADI methods for heat equations with discontinuities along an arbitrary interface. Proc. Symp. Appl. Math. W. Gautschi, editor,  48,  311--315. AMS, 1993, with A. Mayo

138.       Perturbation theorems of eigenvectors.  Numer. Math., a Journal of Chinese Universities, 12(1990), No.3, pp. 284--289, with K. Huang.

139.       Uniform treatment of linear systems -- algorithm and numerical stability. Numer. Comput. Appl. 2: 71-86, 1989.

140.       A generalized conjugate gradient method for solving real skew-symmetric systems. J. on Numer. Methods & Comput. Appl., 8(1987), No.4, pp. 31--37.

141.       An equivalent theorem on the numerical stability for an algorithm, Numer. Math., a Journal of Chinese Universities, 9(1987), No. 1,  pp. 59--65,  with K. Huang

142.       Round off error analysis for polynomial interpolation.  Research and Review in Mathematics, 1989, No. 2, with K. Huang.

143.       On the relation between the behavior and the distribution of the zeros of a polynomial. J. of Nanjing University, Mathematics. Biquarterly, 2(1985), No. 1, pp. 53--59, with K. Huang.

144.       Optimal conjugate gradient method for solving arbitrary linear equations. J. of Nanjing Normal University. 1988, No. 3, pp. 28--34.

145.       Round-off error analysis for a class of conjugate gradient methods with restarting.  J. of Nanjing Normal University. 1986, No. 1, pp. 26--34.

146.       The effect of deflation on the condition number of zeros of polynomials. J. of Nanjing Normal University. 1986, No. 2, pp. 31--37.


147.  Autophobic Spreading of Drops,  J. of Comput. Physics,  Vol. 183, No. 2, pp. 335-366, 2002, with J. K. Hunter, and H. Zhao

148.  New Formulations for Interface Problems in Polar coordinates,  SIAM J. Sci. Comput.,  25, No 1, 224-245, (2003) , with W. Wang, I Chern, and M. Lai

149.  The immersed interface/multigrid methods for interface problems, SIAM J. Sci. Comput.,  Vol. 24,  No.2,  pp. 463 - 479, 2002, with L. Adams.