Skip to main content

Galerkin approximations of a class of nonlinear boundary-value problems and evolution problems in elasticity

  • Non-linear Problems, Finite Elements
  • Conference paper
  • First Online:
Book cover Computing Methods in Applied Sciences

Part of the book series: Lecture Notes in Physics ((LNP,volume 58))

  • 139 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Browder, F., “On the Unification of the Calculus of Variations and the Theory of Monotone Nonlinear Operators in Banach Spaces,” Proc. Nat’l. Acad. Sc., Vol. 56, 1966, pp. 419–425.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Oden, J. T. and Wellford, L. C. Jr., “Finite Element Approximations of a Class of Nonlinear Two-Point Boundary-Value Problems in Finite Elasticity,” TICOM Report, 74-5, Austin, 1974.

    Google Scholar 

  3. Aubin, J. P., “Evaluation des erreurs de troncature des approximations des espaces de Sobolev,” J. Math. Anal. Appl., 21, 1968, pp. 356–368.

    Article  MATH  MathSciNet  Google Scholar 

  4. Nitsche, J., “de+Ein Kriterium fur die quasi-optimalitat des Ritzschen verfahrens,” Numer. Math., 11, 1968, pp. 346–348

    Article  MATH  MathSciNet  Google Scholar 

  5. Oden, J. T. and Wellford, L. C. Jr., “Some Finite Element Methods for the Analysis of Shock and Acceleration Waves in Nonlinear Materials,” Finite Element Analysis of Transient Structural Behavior, Winter Annual Meeting, ASME, Houston, 1975.

    Google Scholar 

  6. Wellford, L. C. Jr. and Oden, J. T., “A Theory of Discontinuous Finite Element Galerkin Approximations of Shock Waves in Nonlinear Elastic Solids I. Variational Methods for Nonli.near Waves,” Computer Methods in Applied Mechanics and Engineering, Vol. 7, No. 1 (to appear).

    Google Scholar 

  7. Wellford, L. C. Jr. and Oden, J. T., “A Theory of Discontinuous Finite Element Galerkin Approximations of Shock Waves in Nonlinear Elastic Solids II. Accuracy and Convergence,” Computer Methods in Applied Mechanics and Engineering, Vol. 7, No. 2 (to appear).

    Google Scholar 

  8. Wellford, L. C. Jr. and Oden, J. T., “Discontinuous Finite Element Approximations for the Analysis of Shock Waves in Nonlinearly Elastic Solids,” Journal of Computational Physics (to appear).

    Google Scholar 

  9. Oden, J. T. and Wellford, L. C. Jr., “Discontinuous Finite Element Approximations for the Analysis of Acceleration Waves in Elastic Solids,” The Mathematics of Finite Elements with Applications, Brunel University, Uxbridge, England, April, 1975 (to be published by Academic Press, London).

    Google Scholar 

  10. Ogden, R. W., “Large deformation isotropic elasticity-on the correlation of theory and experiment for compressible rubberlike solids,” Proc. R. Soc. London, A. 328, pp. 567–583, 1972.

    Article  MATH  ADS  Google Scholar 

  11. Oden, J. T. and Nicolau del Roure, R., “Accuracy and Convergence of Certain Finite Element Approximations of Problems in Nonlinear Elasticity,” (in preparation).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

R. Glowinski J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Oden, J.T. (1976). Galerkin approximations of a class of nonlinear boundary-value problems and evolution problems in elasticity. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences. Lecture Notes in Physics, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120589

Download citation

  • DOI: https://doi.org/10.1007/BFb0120589

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08003-9

  • Online ISBN: 978-3-540-37550-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics