The convergence of a Galerkin approximation scheme for an extensible beam
ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 4, pp. 597-613. 
@article{M2AN_1989__23_4_597_0,
     author = {Geveci, Tunc and Christie, Ian},
     title = {The convergence of a {Galerkin} approximation scheme for an extensible beam},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {597--613},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {23},
     number = {4},
     year = {1989},
     mrnumber = {1025074},
     zbl = {0727.73093},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1989__23_4_597_0/}
}
TY  - JOUR
AU  - Geveci, Tunc
AU  - Christie, Ian
TI  - The convergence of a Galerkin approximation scheme for an extensible beam
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1989
SP  - 597
EP  - 613
VL  - 23
IS  - 4
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1989__23_4_597_0/
LA  - en
ID  - M2AN_1989__23_4_597_0
ER  - 
%0 Journal Article
%A Geveci, Tunc
%A Christie, Ian
%T The convergence of a Galerkin approximation scheme for an extensible beam
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1989
%P 597-613
%V 23
%N 4
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1989__23_4_597_0/
%G en
%F M2AN_1989__23_4_597_0
Geveci, Tunc; Christie, Ian. The convergence of a Galerkin approximation scheme for an extensible beam. ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 4, pp. 597-613. http://www.numdam.org/item/M2AN_1989__23_4_597_0/

[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. | Numdam | MR | Zbl

[2] J. M. Ball, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. | MR | Zbl

[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. | MR | Zbl

[4] R. Courant & D. Hilbert, Methods of Mathematical Physics, Vol. 1, Wiley-Interscience, New York, 1953. | MR | Zbl

[5] R. W. Dickey, Free vibrations and dynamic buckling of an extensible beam, Math. Anal. Appl. 29 (1970), 443-454. | MR | Zbl

[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. | MR | Zbl

[7] P. Holmes & J. Marsden, Bifurcation to divergence and flutter in flow-induced oscillations : An infinite dimensional analysis, Automatica 14 (1978), 367-384. | MR | Zbl

[8] J. Rauch, On convergence of the finite element method for the wave equation, SIAM J. Numer. Anal. 22 (1985), 245-249. | MR | Zbl

[9] J. M. Sanz-Serna, Methods for the numerical solution of the nonlinear Schroedinger equation, Math. Compt. 43 (1984), 21-27. | MR | Zbl

[10] G. Strang & G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973. | MR | Zbl

[11] V. Thomée, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Compt. 34 (1980), 99-113. | MR | Zbl

[12] V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer lecture Notes in Mathematics v. 1054, Springer-Verlag, Berlin, 1984. | MR | Zbl

[13] S. Woinowsky-Krieger, The effect of the axial force on the vibration of hinged bars, J. Appl. Mech, 17 (1950), 35-36. | MR | Zbl