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Theory of mixed and hybrid finite-element approximations in linear elasticity

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Part of the Lecture Notes in Mathematics book series (LNM,volume 503)

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References

  1. Prager, W. and Synge, J. L., “Approximations in Elasticity Based on the Concept of Function Space,” Q. Appl. Math., Vol. 5, No. 3, pp. 241–269, 1943.

    MathSciNet  MATH  Google Scholar 

  2. Herrmann, L. R., “A Bending Analysis of Plates,” Proc. Conf. Matrix Meth. Struct. Mech., Wright-Patterson AFB, Ohio, AFFDL-TR66-80, 1965.

    Google Scholar 

  3. Reissner, E., “On a Variational Theorem in Elasticity,” J. Math. Phys., Vol. 29, pp. 90–95, 1950.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Pian, T. H. H., and Tong, P., “Basis of Finite Element Methods for Solid Continua,” Int. J. Num. Meth. in Eng., Vol. 1, No. 1, pp. 3–28, 1969.

    CrossRef  MATH  Google Scholar 

  5. Oden, J. T. and Reddy, J. N., Variational Methods in Theoretical Mechanics, Springer-Verlag, Heidelberg, Berlin, and New York, (to appear).

    Google Scholar 

  6. Oden, J. T. and Reddy, J. N., “On Mixed Finite Element Approximations,” SIAM J. Num. Anal., (to appear).

    Google Scholar 

  7. Reddy, J. N. and Oden, J. T., “Mathematical Theory of Mixed Finite Element Approximations,” Q. Appl. Math. (to appear).

    Google Scholar 

  8. Ciarlet, P. G. and Raviart, P. A., “Mixed Finite Element Method for the Biharmonic Equations,” Mathematical Aspects of Finite Elements in Partial Differential Equations, Ed. by C. deBoor, Academic Press, N. Y., pp. 125–145, 1947.

    Google Scholar 

  9. Johnson, C., “On the Convergence of a Mixed Finite-Element Method for Plate Bending Problems,” Num. Math., Vol. 21, pp. 43–62, 1973.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Raviart, P. A., “Hybrid Finite Element Methods for Solving 2nd Order Elliptic Equations,” Report, Universite Paris VI et Centre National de la Recherche Scientifique, 1974.

    Google Scholar 

  11. Thomas, J. M., “Methodes des Elements Finis Hybrides Duaux Pour les Problems Elliptiques du Second-Order,” Report 189, Universite Paris VI et Centre National de la Recherche Scientifique, 1975.

    Google Scholar 

  12. Babuska, I., Oden, J. T., and Lee, J. K., “Mixed-Hybrid Finite-Element Approximations of Second-Order Elliptic Boundary Value Problems,” (to appear).

    Google Scholar 

  13. Babuska, I., “Error Bounds for Finite Element Method,” Num. Math., Vol. 16, pp. 322–333, 1971.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Babuska, I. and Aziz, A. K., “Survey Lectures on the Mathematical Theory of Finite Elements,” The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Ed. by A. K. Aziz, Academic Press, N. Y., pp. 3–395, 1972.

    CrossRef  Google Scholar 

  15. Oden, J. T. and Reddy, J. N., An Introduction to the Mathematical Theory of Finite Elements, Wiley Interscience, New York, (to appear).

    Google Scholar 

  16. Hlavacek, I. and Necas, J., “On Inequalities of Korn’s Type,” Arch. Rat. Mech. Anal., Vol. 36, pp. 305–334, 1970.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Nitsche, J., “Ein Kriterium fur die Quasi-Optimalitat des Ritzchen Verfahrens,” Num. Math., Vol. 11, pp. 346–348, 1968.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Kondratev, V. A., “Boundary Problems for Elliptic Equations with Conical or Angular Points,” Trans. Moscow Math. Soc. 1967, pp. 227–313.

    Google Scholar 

  19. Babuska, I., “The Finite Element Method with Lagrange Multipliers,” Num. Math., Vol. 20, pp. 172–192, 1973.

    CrossRef  Google Scholar 

  20. Lee, J. K., “A-Priori Error Estimates of Mixed and Hybrid Finite Element Methods,” Ph.D. Dissertation, Div. of Engr. Mech., Univ. of Texas Austin (forthcoming).

    Google Scholar 

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Oden, J.T., Lee, J.K. (1976). Theory of mixed and hybrid finite-element approximations in linear elasticity. In: Germain, P., Nayroles, B. (eds) Applications of Methods of Functional Analysis to Problems in Mechanics. Lecture Notes in Mathematics, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088747

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  • DOI: https://doi.org/10.1007/BFb0088747

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