Skip to main content
Log in

Error estimates in finite element approximations for problems in linear elasticity Part 2. Problems in elastodynamics; continuous time approximations

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Tong, P., & T. Pian, The convergence of the finite element method in solving linear elastic problems, Int. J. Solids Structures 3, 865–879 (1967).

    Google Scholar 

  2. Key, S.W., A convergence investigation of the direct stiffness method, Ph. D. thesis, University of Washington 1966.

  3. Johnson, M.W., & R.W. McLay, Convergence of the finite element method in the theory of elasticity, J. Appl. Mech. 35, 274–278 (1968)

    Google Scholar 

  4. Carlson, R.E., & C.A. Hall, Ritz approximations to two-dimensional boundary value problems, Numer. Math. 18, 171–181 (1971)

    Google Scholar 

  5. Babuska, I., & A.K. Aziz, Lectures on mathematical foundations of the finite element method, in Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, edited by A.K. Aziz, Acad. Press 1972.

  6. Aliev, B., A difference scheme for the solution of the second boundary state problem of the theory of elasticity, USSR Comp. Math. Math. Phy. 10, 171–182 (1972)

    Google Scholar 

  7. Desai, C.S., & J.F. Abel, Introduction to the Finite Element Method, Van Nostrand 1972.

  8. Strang, G., & G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall 1973.

  9. Oden, J. T., & J. N. Reddy, An Introduction to the Mathematical Theory of Finite Elements, John Wiley 1976.

  10. Fichera, G., Linear Elliptic Differential Systems and Eigenvalue Problems, Lecture Notes Series Vol. 8 Springer 1965.

  11. Fichera, G., Existence Theorems in Elasticity, in Handbuch der Physik, Band VI a/2, edited by C. Truesdell, Springer 1972

  12. Ciarlet, P.G., & P.A. Raviart, General Lagrange and Hermite interpolation in R n with applications to finite element method. Arch. Rational Mech. Anal. 46, 177–199 (1972)

    Google Scholar 

  13. Strang, G., Approximation in the finite element method, Numer. Math. 19, 81–98 (1972).

    Google Scholar 

  14. Nitsche, J., Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math. 11, 346–348 (1968).

    Google Scholar 

  15. Chou, S.-I., Galerkin approximations on linear elastostatics, elastodynamics, and thermoelastodynamics, Ph. D. thesis, Rice University 1972.

  16. Lions, J.L., Equations Différentielles Operationelles et Problème aux Limites, Springer 1961.

  17. Bellman, R., Stability Theory of Differential Equations, McGraw-Hill 1952.

  18. Dupont, T., ℒ2-estimates for Galerkin methods for second order hyperbolic equations, SIAM J. Numer. Anal. 10, 880–889 (1973)

    Google Scholar 

  19. Douglas, J., & T. Dupont, Galerkin methods for parabolic equations, SIAM J. Numer. Anal. 7, 575–626 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chou, S.I., Wang, C.C. Error estimates in finite element approximations for problems in linear elasticity Part 2. Problems in elastodynamics; continuous time approximations. Arch. Rational Mech. Anal. 72, 155–174 (1979). https://doi.org/10.1007/BF00249362

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00249362

Keywords

Navigation