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On the simplified hybrid-combined method


Authors: Zi Cai Li and Guo Ping Liang
Journal: Math. Comp. 41 (1983), 13-25
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1983-0701621-7
MathSciNet review: 701621
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Abstract: In order to solve the boundary value problems of elliptic equations, especially with singularities and unbounded domains, the simplified hybrid-combined method, which is equivalent to the coupling method of Zienkiewicz et al. [15], is presented. This is a combination of the Ritz-Galerkin and the finite element methods. Its optimal error estimates are proved in this paper, and the solution strategy of its algebraic equation system is discussed.


References [Enhancements On Off] (What's this?)

  • [1] S. Bergman, Integral Operations in the Theory of Linear Partial Differential Equations, Springer-Verlag, Berlin and New York, 1969. MR 0239239 (39:596)
  • [2] I. Babuška & A. K. Aziz, "Survey lectures on the mathematical foundations of the finite element method," in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Ed.), Academic Press, New York and London, 1972, pp. 3-359. MR 0421106 (54:9111)
  • [3] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 0520174 (58:25001)
  • [4] S. C. Eisenstat, On the Rate of Convergence of the Bergman-Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems, Research Report No. 72-2, Department of Computer Science, Yale University, 1972.
  • [5] G. J. Fix, "Hybrid element method," SIAM Rev., v. 18, 1976, pp. 460-484. MR 0416066 (54:4142)
  • [6] C. Johnson & C. Nedelec, "On the coupling of boundary integral and finite element methods," Math. Comp., v. 35, 1980, pp. 1063-1079. MR 583487 (82c:65072)
  • [7] Z. C. Li & G. P. Liang, "On Ritz-Galerkin-F.E.M. combined method of solving the boundary value problems of elliptic equations," Sci. Sinica, v. 24, 1981, pp. 1497-1508. MR 655947 (83d:65293)
  • [8] J. L. Lions & E. Magènes, Problèmes aux Limites non Homogènes et Applications, Vol. 1, Travaux et Recherches Mathematiques, no. 17, Dunod, Paris, 1968. MR 0247243 (40:512)
  • [9] P. A. Raviart & J. M. Thoms, "Primal hybrid finite element method for 2nd order elliptic equations," Math. Comp., v. 31, 1977, pp. 391-413. MR 0431752 (55:4747)
  • [10] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Transl. Math. Monos., vol. 7, Amer. Math. Soc., Providence, R.I., 1963.
  • [11] G. Strang & G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973. MR 0443377 (56:1747)
  • [12] A. N. Tikhonov & A. A. Samarskii, Equations of Mathematical Physics (Transl. by A. P. N. Robson & P. Basu), Macmillan, New York, 1973. MR 0165209 (29:2498)
  • [13] P. Tong, T. H. H. Pian & S. J. Lasry, "A hybrid element approach to crack problems in plane elasticity," Internat. J. Numer. Methods Engrg., v. 7, 1973, pp. 297-308.
  • [14] I. N. Vekua, New Method for Solving Elliptic Equations, North-Holland, Amsterdam, 1967.
  • [15] O. C. Zienkiewicz, D. W. Kelly & P. Bettess, "The coupling of the finite element method and boundary solution procedures," Internat. J. Numer. Methods Engrg., v. 11, 1977, pp. 355-375. MR 0451784 (56:10066)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0701621-7
Article copyright: © Copyright 1983 American Mathematical Society

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