论著目录:

(*.ps or *.pdf files for some papers are available in the preprint version, for the published version please find in the corresponding journals)

1. Zhiping Li (1986), The finite element method for boundary value problems of nonlinear three-dimensional elasticity,  东北数学, 2(4), pp.449-467.

2. 李治平 (1987), 抛物型方程在奇异摄动下的周期解,     数学物理学报, 7(1), pp.31-43.

3. Zhiping Li (1989), Existence theorem and finite element method for static problems of a class of hyperelastic shells}, Chin. Ann. of Math., 10B(2), pp.169-189.

4. Zhiping Li (1989), The finite element method for nonlinear elasticity, J. Comp. Math., 7(1), pp.1-14.

5. Zhiping Li (1990), The finite element incremental method for nonlinear elasticity, 东北数学, 6(1), pp.93-100.

6. Zhiping Li (1991), Positive finite element solutions for semi-linear elliptic equations, 东北数学, 7(1), pp.63-80.

7. Zhiping Li (1991), Globally 1-1 solutions and finite element method for elastic contact problems in nonlinear elasticity, 东北数学, 7(2), pp.158-169.

8. Zhiping Li (1992), Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon, Proc. R. Soc. Lond., 439A, pp.131-137.

9. Zhiping Li (1995), Element removal method for singular minimizers in hyperelasticity, Math. Models Methods Appli. Sci., 5(3), pp.387-399. (pdf file)

10. Zhiping Li and Martin Reed (1995), A finite element method to model progressive fracturing, Comput. Methods Appl. Mech. Engrg., 120, pp.303-313.

11. Zhiping Li and Martin Reed (1995), Convergence analysis for an element-by-element finite element method, Comput. Methods Appli. Mech. Engrg., 123, pp.33-42.

12. Zhiping Li (1995), A numerical method for computing singular minimizers, Numer. Math., 71, pp.317-330. (pdf file)

13. Zhiping Li (1996), A theorem on lower semicontinuity of integral functionals,  Proc. R. Soc. Edin., 126A, pp.363-374. (pdf file

14. Zhiping Li (1996), Existence of minimizers and microstructure in nonlinear elasticity, Nonlinear Analysis, 27(3), pp.297-308. (pdf file)

15. Zhiping Li (1996), Lower semicontinuity of multiple integrals and convergent integrands, ESAIM: Control, Optimi. Calculus Variat., 1, pp.169-189. (pdf file)

16. Zhiping Li (1996), Numerical methods for minimizers and microstructures in nonlinear elasticity, Math. Models Methods Appl. Sci., 6(7), pp.957-975. (pdf file)

17. Zhiping Li (1997), Simultaneous numerical approximation of microstructures and relaxed minimizers. Numer. Math., 78(1), pp.21-38. (pdf file)

18. Zhiping Li (1998), Laminated microstructure in a variational problem with a non-rank-one connected double well potential.  J. Math. Anal. Appl., 217, pp.490-500. (pdf file)

19. Zhiping Li (1998), An integral representation theorem for lower semicontinuous envelopes of integral functionals. Nonliear Analysis 32(4), pp.541-548. (pdf file)

20. Zhiping Li(1998), Rotational transformation method and some numerical techniques for computing microstructures.  Math. Models Meth. Appl. Sci., 8(6), pp.985-1002. (pdf file)

21. Zhiping Li (2000), A Periodic relaxationmethod for computing microstructures. Appl. Numer. Math., 32, pp. 291-303. (ps file)

22. Zhiping Li (2000), A coupled numerical method for relaxed minimizers and inhomogeneous microstructures. In  Proceedings of 4th International Conference/Exhibition on High Performance Computing in Asia-Pacific Region, Volume II, IEEE Computer Society, pp. 1022-1024. (ps file)

23. Zhiping Li (2000),Finite order rank-one convex envelopes and computation of microstructures with laminates in laminates. BIT, 40(4), pp.745-761. (ps file)

24. Zhiping Li (2001), Mesh transformation and regularization in numerical simulation of     austenitic-martensitic phase transition}. Computational Materials Science 21(2001), pp. 418-428. (ps file)

25. Zhiping Li (2001), A mesh transformation method for computing microstructures. Numer. Math., 89(3), pp. 511-533. (pdf file)

26. Zhiping Li (2001), Computations of needle-like microstructures. Appl. Numer. Math., 39, pp. 1-15. (pdf file)

27. Zhiping Li (2002), Numerical justification of branched laminated microstructure with surface energy. SIAM. J. Sci. Comput, 24 (3) (Jan. 2003), pp. 1054-1075. (ps file)

28. Zhiping Li (2003), A numerical study on the scale of laminated microstructure with surface energy. Materials Sci. & Eng.,343, pp. 182-193.  (pdf file)

29. 李治平 (2003), 晶体微观结构的数值计算数学进展, 323, pp. 257-268. (ps file)

30. Xinwei Yu, Zhiping Li and Lung-An Ying (2003) , Singular perturbation of a class of non-convex functionals. Nonlinear Analsis - Theory Methods & Applications, 52(4), pp. 1129-1152. (ps file)

31. Zhiping Li (2004), Numerical computation of stress induced microstructure. Science in China, series A, vol. 47, supp., pp. 165-171.  (pdf file)

32. Zhiping Li (2004), Multiscale modelling and computation of  microstructures in multi-well problems. Math. Mod. Meth. Appl. Sci., 14(9), 1343-1360.  (pdf file)

33. Zhiping Li and Xiaonan Wu (2004), Multi-atomic Young measure and artificial boundary in approximation of micromagnetics. Appl. Numer. Math., 51(1), 69-88.  (pdf file)

34. Zhiping Li (2005), A regularized mesh transformation method for the computation of crystalline microstructures. Mathematical and Computer Modelling, 41(8-9), 903-914.(DOI:10.1016/j.mcm.2004.08.006) (pdf file)

35. Jiansong Zhou and Zhiping Li (2005), Computing Non-smoothminimizers with the mesh transformation method. IMA J. Numer. Anal., 25, 458-472. (DOI: 10.1093/imanum/dri002) (pdf file) 

36. Zhiping Li (2006), The mesh transformation method and optimal finite element solutions. BIT NUMERICAL MATHEMATICS 46 (1): 85-95. (pdf file) 

37. Yu Bai and Zhiping Li (2006), A truncation method for detecting singular minimizers involving the Lavrentiev phenomenon. Math. Mod. Meth. Appl. Sci., 16(6), 847-867. (pdf file)

38. Liying Liu and Zhiping Li (2007), Computation of length scales for second-order laminated microstructure with surface energy. Appl. Math. Modelling, 31, 245-258. (DOI: 10.1016/j.apm.2005.10.001) (pdf file)

39. Wang Xin and Zhiping Li (2007), A numerical iterative scheme for computing finite order rank-one convex envelopes. 
Appl. Math. Comp., 18, 19-30. (DOI: 10.1016/j.amc.2006.06.088) (pdf file)

40. Yu Bai and Zhiping Li (2007), Numerical Solution of nonlinear elasticity problems with Lavrentiev phenomenon. Math. Mod.
Meth. Appl. Sci., 17
(10), 1619-1640.  (pdf file)

41. Zhiping Li and Carsten Carstensen (2007), An averaging scheme for macroscopic numerical simulation of nonconvex minimization problems. BIT Numerical Math., 47, 601-611.  (pdf file

42. Zhiping Li (2008), Computation of the lower semicontinuous envelope of integral functionals and non-homogeneous microstructures. Nonlinear Analysis, 68(7) (April 2008), 2058-2071. (http://dx.doi.org/10.1016/j.na.2007.01.031) (pdf file)

43. Zhiping Li (2009), Numerical analysis and computation of a multi-order laminated microstucture, Applied   Mathematical Modelling, 33, 81-91. . (DOI:10.1016/j.apm.2007.10.019) (pdf file)

44. Zhiping Li and Xianmin Xu (2009), Convergence and Stability of a Numerical Method for Micromagnetics, Numer. Math., 112(2), 245-265. (DOI: 10.1007/s00211-009-0210-1) (pdf file)

45. Xianmin Xu  and Zhiping Li (2009),Non-Conforming Finite Element and Artificial Boundary in Multi-atomic Young Measure Approximation for Micromagnetics, Appl. Numer. Math. 59, 920-937. (DOI: 10.1016/j.apnum.2008.03.037) (pdf file)

46. Wei Jiang and Zhiping Li (2009), A numerical study of the wrinkling evolution of an elastic film on a  viscous layer, Modelling Simul. Mater. Sci. Eng. , 17, 055010. (DOI:10.1088/0965-0393/17/5/055010) (pdf file)

47.  Xianmin Xu and Zhiping Li  ( 2009), A Posteriori Error Estimates of a Non-conforming Finite Element Method for Problems with Artificial Boundary Conditions, J. Comp. Math., 27(6), 677-696.  (DOI: 10.4208//jcm.2009.09-m2608) (pdf file) 

48. Zhiping Li and Dali Men (2010), Pin-pointing the phase boundary with the mesh transformation method in a relaxed double-well problem, Proceedings of the 12th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS'10),May 3-6,2010, Kantaoui, Sousse, Tunisia, pp.15-20.

49. Shan Wang and Zhiping Li (2011), Mathematical modeling and numerical simulation of telephone cord buckles of elastic films. Sci. China Math., 54(5) 2011: 1063-1076, doi: 10.1007/s11425-011-4172-2. (pdf file)

50. Yijiang Lian and Zhiping Li (Oct., 2011), A dual-parametric finite element method for cavitation in nonlinear elasticity. J. Comput. Appl. Math., 236 (5) 2011,834-842. doi:10.1016/j.cam.2011.05.020. (pdf file)

 

51. Shan Wang and Zhiping Li (Oct., 2011), Evaluation of mechanical parameters of an elastic thin film system by modeling and numerical simulation of telephone cord buckles. J. Comput. Appl. Math., 236 (5) 2011, 860-866. doi:10.1016/j.cam.2011.05.018. (pdf file)

 

52. Yijiang Lian and Zhiping Li (Dec., 2011), A Numerical Study on Cavitation in

Nonlinear Elasticity Defects and Configurational Forces. Math. Mod. Meth.

Appl. Sci., 21(12), 2551-2574. doi: 10.1142/S02 18202511005830. (pdf file)

 

53. Yijiang Lian and Zhiping Li (2012), Position and size effects on voids growth in nonlinear elasticity. Int. J. Fracture, 173(2), 147-161. doi: 10.1007/s10704-011-9674-y. (pdf file)

 

54. Shan Wang and Zhiping Li, A multiple-endpoints Chebyshev collocation method for high order differential equations. Contemporary Mathematics, Volume 586 (2013), 365-373. doi: http://dx.doi.org/10.1090/ conm/586/11610. (pdf file)

 

55. Chunmei Su and Zhiping Li, Error Analysis of a Dual-parametric Bi-quadratic FEM in Cavitation Computation in Elasticity, SIAM J. Numer. Anal. 53 (3) (2015), pp. 1629-1649. http://dx.doi.org/ 10.1137/140971142. (pdf file)

 

56. Chunmei Su and Zhiping Li, Mathematical theory and numerical computation of cavitation in nonlinear elasticity (in Chinese).

Sci Sin Math, 46 (2016), pp. 10711094. doi: 10.1360/N012015-00153.

 

57. Chunmei Su and Zhiping Li, Orientation-Preservation Conditions on an Iso-parametric FEM in Cavitation Computation. Sci China Math., 60(2017), 719-734. doi: 10.1007/s11425-016-0019-0.

 

58. A meshing strategy for a quadratic iso-parametric FEM incavitation computation in nonlinear elasticity, Journal of Computational and Applied Mathematics 330 (2018) 630647. http://dx.doi.org/10.1016/j.cam.2017.09.006.(Chunmei Su and Zhiping Li)

 

59. Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity, Front. Math. China 2018, 13(1): 203226. https://doi.org/10.1007/ s11464-017-0664-x. (Liang Wei and Zhiping Li)

60. A numerical study on dynamics of cavity growth in nonlinear elasticity, International Journal of Fracture, 214 (2) (2018), 105-113. doi: https://doi.org/ 10.1007/s10704-018-0321-8.  (Lufan Long and Zhiping Li)

61. A numerical study on bifurcations in multi-void growth in nonlinear elasticity. International Journal of Fracture, 214 (2) (2018), 129-137. doi:  https://doi.org/10.1007/s10704-018-0323-6.  (Weijie Huang and Zhiping Li)

62. A locking-free FEM for cavitation computation in nearly incompressible nonli- near elasticity,  J. Comp. Appl. Math., 353 (2019), 210-218.  https://doi.org/10.1016/j.cam.2018.12.019. (Weijun Ma and Zhiping Li)

63. A mixed finite element method for multi-cavity computation in incompressible nonlinear elasticity, J. Comp. Math., 37 (2019) (5), 611-630. https://doi.org/10. 4208/jcm.1807-m2018-0137.(Weijie Huang and Zhiping Li)

64. A locking-free DP-Q2-P1 MFEM for incompressible nonlinear elasticity problems, Numer. Math.: Theory, Meth. Appl., 12 (2019) (4), 995-1011. doi: 10.4208/nmtma.OA-2018-0087. (Weijie Huang and Zhiping Li)

 

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