The convergence of a Galerkin approximation scheme for an extensible beam

Tunc Geveci; Ian Christie

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 4, page 597-613
  • ISSN: 0764-583X

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Geveci, Tunc, and Christie, Ian. "The convergence of a Galerkin approximation scheme for an extensible beam." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.4 (1989): 597-613. <http://eudml.org/doc/193581>.

@article{Geveci1989,
author = {Geveci, Tunc, Christie, Ian},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {stability; transverse displacement; hinged ends; semi-discrete Galerkin approximate scheme; rate of convergence; error estimates; Crank-Nicolson time discretization},
language = {eng},
number = {4},
pages = {597-613},
publisher = {Dunod},
title = {The convergence of a Galerkin approximation scheme for an extensible beam},
url = {http://eudml.org/doc/193581},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Geveci, Tunc
AU - Christie, Ian
TI - The convergence of a Galerkin approximation scheme for an extensible beam
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 4
SP - 597
EP - 613
LA - eng
KW - stability; transverse displacement; hinged ends; semi-discrete Galerkin approximate scheme; rate of convergence; error estimates; Crank-Nicolson time discretization
UR - http://eudml.org/doc/193581
ER -

References

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  1. [1] G. A. BAKER & J. H. BRAMBLE, Semidiscrete and single step fully discrete approximations for second order hyperbolic equations, RAIRO Anal. Numer. 13 (1979), 75-100. Zbl0405.65057MR533876
  2. [2] J. M. BALL, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. Zbl0254.73042MR319440
  3. [3] I. CHRISTIE & J. M. SANZ-SERNA, A Galerkin method for a nonlinear integro-differential wave system, Comp. Meth. Appl. Mech. Eng. 44 (1984), 229-237. Zbl0525.73089MR757058
  4. [4] R. COURANT & D. HILBERT, Methods of Mathematical Physics, Vol. 1, Wiley-Interscience, New York, 1953. Zbl0051.28802MR65391
  5. [5] R. W. DICKEY, Free vibrations and dynamic buckling of an extensible beam, Math. Anal. Appl. 29 (1970), 443-454. Zbl0187.04803MR253617
  6. [6] T. GEVECI, On the convergence of Galerkin approximation schemes for second-order hyperbolic equations in energy and negative norms, Math. Compt. 42 (1984), 393-415. Zbl0553.65082MR736443
  7. [7] P. HOLMES & J. MARSDEN, Bifurcation to divergence and flutter in flow-induced oscillations : An infinite dimensional analysis, Automatica 14 (1978), 367-384. Zbl0385.93028MR495662
  8. [8] J. RAUCH, On convergence of the finite element method for the wave equation, SIAM J. Numer. Anal. 22 (1985), 245-249. Zbl0575.65091MR781318
  9. [9] J. M. SANZ-SERNA, Methods for the numerical solution of the nonlinear Schroedinger equation, Math. Compt. 43 (1984), 21-27. Zbl0555.65061MR744922
  10. [10] G. STRANG & G. J. FIX, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973. Zbl0356.65096MR443377
  11. [11] V. THOMÉE, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Compt. 34 (1980), 99-113. Zbl0454.65077MR551292
  12. [12] V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Springer lecture Notes in Mathematics v. 1054, Springer-Verlag, Berlin, 1984. Zbl0528.65052MR744045
  13. [13] S. WOINOWSKY-KRIEGER, The effect of the axial force on the vibration of hinged bars, J. Appl. Mech, 17 (1950), 35-36. Zbl0036.13302MR34202

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