The Publication of Prof. Zhong-Ci SHI

Books and Papers

  1. A covering theorem on bounded schlicht functions, Advances in Mathematics, 2, 657--677, 1956.
  2. Asymptotic behaviour of eigenfunctions for Sturm--Liouville problems, computed by the perterbation method, Doklady Akad. Nauk, USSR, 131, 1279-1282, 1960 (in Russian).
  3. Note on the computation of the first eigenvalue of symmetrical operators by Ritz-Galerkin method, Sbornik Vychisl. Mat., Akad. Nauk, USSR, 6, 84-86, 1960 (in Russian).
  4. Fehlerabschatzung fur das Ritz-Galerkinsche Verfahren, ZAMM, 40, Heft 5/6, 286, 1960.
  5. A necessary condition for the convergence of certain stationary iterations, Collection of papers on the fifth anniversary of University of Science and Technology of China, 41--43, 1963.
  6. Bounds for the p-condition number of matrices with positive eigenvalues, Acta Mathematica Sinica, 14, 790-796, 1964.
  7. Bounds for determinants, eigenvalues and the condition number of certain types of matrices, Ibid, 15, 324-341, 1965 (with Buo-Ying Wang).
  8. Upper and lower bounds for all eigenvalues of the neutron transport equations, Applied and Numerical Mathematics, 2, 141-151, 1965 (with Qun Lin).
  9. Bounds for determinants, J. of Sichuan Univ., 2, 19-24, 1965.
  10. Upper bounds for eigenvalues of certain integral equations, J. of Univ. of Science and Technology of China, 3, 1-4, 1973.
  11. On the convergence of a difference scheme for the biharmonic equation, Ibid, 5, 34-39, 1975.
  12. An analysis of the internal forces of a shell type curved sluice gate, Ibid, 5, 57-74, 1975.
  13. Finite element analysis for steel plate sluice gates, Tech. report, Bureau of Water Conservancy, Anhui Province, No. 1, 1-58, 1975.
  14. Approximate solution of plate bending problems using the bicubic cardinal splines, J. of USTC, 6, 8-17, 1976.
  15. Spline finite element method, Mathematica Numerica Sinica, 1, 50-72, 1979.
  16. Relationship between thick and thin plates with simply supported edges, Ibid, 1, 179-188, 1979 (with Yi-Shen Li).
  17. Finite element implementation for the link conditions of composite elastic structures, Numerical Methods and Computer Applications, 1, 211-216, 1980.
  18. Free vibration of simply supported Reissner thick plates, Acta Mathematica Applicata Sinica, 4, 53-62, 1981 (with Yi-Shen Li).
  19. Comments on the paper "Inequalities for Hermitian matrices", J. of USTC, 11, 128-131, 1981.
  20. Note on nonsingularity of the interpolating matrix of cubic splines, Math. Numer. Sinica, 5, 195-203, 1983.
  21. Certain convergence criteria for nonconforming finite elements, Workshop "Diskre-ti-si-erungen in der kontinumsmechanik", Bad Honnef, 1983 (with F. Stummel).
  22. On the convergence properties of the quadrilateral elements of Sander and Beckers, Mathematics of Computation, 42, 493-504, 1984.
  23. A convergence condition for the quadrilateral Wilson element, Numerische Mathematik, 44, 349-361, 1984.
  24. An explicit analysis of Stummel's patch test examples, Inter. J. Numer. Meths. Eng., 20, 1233--1246, 1984.
  25. On the convergence rate of the boundary penalty method, Ibid, 20, 2027-2032, 1984.
  26. The generalized patch test for Zienkiewicz's triangles, J. of Computational Mathematics, 2, 279-286, 1984.
  27. Difficulties with Iron's patch test, ZAMM, 64, 314-315, 1984.
  28. On the convergence of nonconforming finite elements, Proc. of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, ed.K.Feng, Science Press, 78-95, 1984.
  29. Convergence properties of two nonconforming finite elements, Computer Meths. Appl. Mech. Eng., 48, 123-137, 1985.
  30. On the convergence of an incomplete biquadratic plate element, Math. Numer. Sinica, 8, 53-62, 1986.
  31. A remark on the optimal order of convergence of Wilson's nonconforming element, Ibid, 8, 159-163, 1986.
  32. A unified formation of shape functions for two kinds of nonconforming plate elements, Ibid, 8, 428-434, 1986.
  33. Convergence of the TRUNC plate element, Computer Meths. Appl. Mech. Eng., 62, 71-88, 1987.
  34. The F-E-M-Test for nonconforming finite elements, Mathematics of Computation, 49, 391-405, 1987.
  35. On the nine degree quasi-conforming plate element, Math. Numer. Sinica, 10, 100-106, 1988.
  36. On Stummel's examples to the patch test, Computational Mechanics, 5, 81-87, 1989.
  37. An analysis of Specht's nine degree plate element, Math. Numer. Sinica, 11, 312-318, 1989.
  38. On a second order quasi-conforming element, Ibid, 11, 442-444, 1989.
  39. A direct analysis of the nine degree quasi-conforming element, Ibid, 12, 76-84, 1990 (with Shao-Chun Chen).
  40. Error analysis of Morley element, Ibid, 12, 113-118, 1990.
  41. On the accuracy of the quasi-conforming and generalized conforming finite elements, Chin. Ann. of Math., 11B, 148-155, 1990.
  42. On the shape function of Bergan's energy-orthogonal plate element, J. of USTC, 20, 127-132, 1990.
  43. Construction and analysis of a new energy-orthogonal plate element, J. of Comput. Math., 8, 75-91, 1990 (with Fei Zhang).
  44. Convergence of a nine parameter generalized conforming element, Math. Numer. Sinica, 13, 75--85, 1991 (with Shao-Chun Chen).
  45. Double set parameter method of constructing stiffness matrices, Ibid, 13, 286-296, 1991 (with Shao-Chun Chen).
  46. On the free formation of constructing stiffness matrices, Ibid, 13, 417-424, 1991 (with Shao-Chun Chen).
  47. Mathematical theory of some unconventional finite element methods, Contemporary Mathematics 163: Computational Mathematics in China (eds. Z.C. Shi and C.C. Yang) 111-125, American Mathematical Society, 1994 (with Ming Wang).
  48. Convergence analysis of Bergan's energy-orthogonal plate element, M^3AS, 4, 489-507, 1994 (with Shao-Chun Chen, Fei Zhang).
  49. A multigrid method for Bergan's energy-othogonal plate element, Proc. 2nd Japan-China Joint Seminar on Numerical Mathematics, Lecture notes in Numer. Appl. Anal.,14, 159-169, 1995 (eds. Z.C. Shi and T. Ushijima), (with Xi-Jun Yu, Zheng-Hui Xie).
  50. Plate elements with high accuracy, Collection of papers dedicated to the 70th birthday of Prof. Chao-hao Gu, World scientific, Singapore,158-164, 1996 (with Shao-chun Chen and Hong-ci Huang).
  51. On the symmetrical form of the 9-parameter double set parameter element and the generalized conforming element, Math. Numer. Sinica,18,422-425, 1996 (with Dongyang Shi).
  52. Substructure preconditioners for nonconforming elements, in Proc. of the 8th International Conference on Domain Decomposition Methods, John Wiley, 109-116, 1997 (eds. R. Glowinski, J. Periaux, Z.-C. Shi and O. Widlund), (with Zheng-hui Xie).
  53. A new superconvergence property of Wilson nonconforming finite element, Mumerishe Mathmatik , 78, 259-268, 1997 (with Bin Jiang and Weimin Xue).
  54. Multigrid method for Wilson nonconforming finite element with numerical integration, Domain Decomposition Methods and Related Topics, RIMS, Kyoto, 103-121, 1997 (with Bin Jiang).
  55. A two-level additive Schwarz method for Morley element on nonnested meshes, Math. Numer. Sinica, 19, 313-328, 1997 (with Zheng-hui Xie).
  56. Intergrid transfer operators for biharmonic problems using nonconforming plate elements on nonnested meshes,Comtemporary Mathematics, 218, 460-467, 1998 (with Zheng-hui Xie).
  57. Substructure preconditioners for nonconforming plate elements, JCM,16, 289-304, 1998 (with Zheng-hui Xie).
  58. Multigrid methods for Morley element on nonnested meshed, JCM, 16, 385-395, 1998 (with Zheng-hui Xie).
  59. Cascadic multigrid method for a plate bending problem, East-West J. of Numerical Mathematics , 6, 137-153, 1998 (with Xue-jun Xu).
  60. Cascadic multigrid method for the second order elliptic problem, East-West J. of Numerical Mathematics, 6, 309-318, 1998 (with Xue-jun Xu).
  61. Convergence of multigrid methods for the Wilson nonconforming finite element, East-West J. of Numerical Mathematics, 6, 1-11, 1999 (with Zhangxin Chen).
  62. A note on equivalence of some triangular plate elements, Math. Numer. Sinica, 21, 39-44, 1999 (with Jiacheng Wang).

Monograph and Books Edited by Z.-C. Shi

  1. The Mathematical Theory of Elastic Structures, Science Press, Beijing, 1981; English Edition by Springer-Verlag & Science Press,1995 (with Kang Feng).
  2. BAIL V, Proceedings of the Fifth International Conference on Boundary and Interior Layer-Computational and Asymptotic Methods, June 20-24, 1988, Shanghai, China, Bools Press (eds. Ben-yu Guo, J.J.H. Miller and Z.-C. Shi).
  3. Procedding of International Conference on Scientific Computation, Hangzhou, China, August 20-23, 1991, Word Scientific (eds. Tony Chan and Z.-C. Shi).
  4. Proceeding of the First China-Japan Seminar on Numerical Mathematics, Beijing, China, August 24-29, 1992, Word Scientific (eds. Z.-C. Shi and Teruo Ushijima).
  5. Proceeding of the International Conference on Computation of Differential Equations and Dynamical Systems, Beijing, China, September 1-5, 1992, World Scientific (eds. Kang Feng and Z.-C. Shi).
  6. Computational Mathematics in China, Contemporary Mathematics 163, American Mathematical Society, 1994 (eds. Z.-C. Shi and C.C. Yang).
  7. Proceedings of Conference on Scientific and Engineering Computing, National Defence Industry Press, Beijing, 1994 (eds. Jun-Zhi Cui, Z.-C. Shi and Dao-Liu Wang).
  8. Proceeding of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical & Applied Mathematics, Kinokuniya, Tokyo, 1995 (eds. Teruo Ushijima, Z.-C. Shi and Takashi Kako).
  9. Computational Methods in Applied Sciences, Science Press, New York, 1996 (eds. Wei Cai, Z.-C. Shi, Chi-Wang Shu and Jinchao Xu).
  10. Proceedings of the Eighth International Conference on Domain Decomposition Methods in Science and Engineering, John Wiley & Sons, 1996 (eds. R. Glowinski, J. Periaux, Z.-C. Shi and O. Widlund).
  11. Proceedings of Third China-Japan Seminar on Numerical Mathematics, Science Press, Beijing, 1998 (eds. Z.-C. Shi and Masatake Mori).
  12. Proceedings of the Fourth Japan-China Seminar on Numerical Mathematics, Kinokuniya, Tokyo, 1999 (eds. Hideo Kawarada, Massaki Nakamura and Z.-C. Shi).

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