Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 63-84. 
@article{M2AN_2000__34_1_63_0,
     author = {Lasiecka, Irena and Marchand, Rich},
     title = {Optimal error estimates for {FEM} approximations of dynamic nonlinear shallow shells},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {63--84},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {1},
     year = {2000},
     mrnumber = {1735976},
     zbl = {0965.74069},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_1_63_0/}
}
TY  - JOUR
AU  - Lasiecka, Irena
AU  - Marchand, Rich
TI  - Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2000
SP  - 63
EP  - 84
VL  - 34
IS  - 1
PB  - Dunod
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_2000__34_1_63_0/
LA  - en
ID  - M2AN_2000__34_1_63_0
ER  - 
%0 Journal Article
%A Lasiecka, Irena
%A Marchand, Rich
%T Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2000
%P 63-84
%V 34
%N 1
%I Dunod
%C Paris
%U http://www.numdam.org/item/M2AN_2000__34_1_63_0/
%G en
%F M2AN_2000__34_1_63_0
Lasiecka, Irena; Marchand, Rich. Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 63-84. http://www.numdam.org/item/M2AN_2000__34_1_63_0/

[1] M. Bernadou, Méthodes d'Éléments Finis pour les Problèmes de Coques Minces. Masson, Paris-Milan-Barcelone (1994).

[2] M. Bernadou and P.G. Ciarlet, Sur l'ellipticité du modèle linéaire de coques de W.T. Koiter, in Computing Methods in Applied Sciences and Engineering (Lecture Notes in Economics and Mathematical Systems), Springer-Verlag (1976) 89-136. | MR | Zbl

[3] M. Bernadou and B. Lalanne, On the approximations of free vibration modes of a general thin shell, application to turbine blades, in The Third European Conference on Mathematics in Industry, J. Manley et al. Eds., Kluwer Academic Publishers and B.G. Teubner Stuttgart (1990) 257-264. | Zbl

[4] M. Bernadou, P.G. Ciarlet and B. Miara, Existence theorems for two-dimensional linear shell theories. Technical Report 1771, Unité de Recherche INRIA-Rocquencourt (1992). | Zbl

[5] M. Bernadou and J.T. Oden, An existence theorem for a class of nonlinear shallow shell problems. J. Math. Pures Appl. 60 (1981) 285-308. | MR | Zbl

[6] P.G. Ciarlet, The Finite Element Method For Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978). | MR | Zbl

[7] M.C. Delfour and J.P. Zolésio, Tangential differential equations for dynamical thin/shallow shells. J. Differential Equations 128 (1995) 125-167. | MR | Zbl

[8] W. Flügge, Tensor Analysis and Continuum Mechanics. Springer-Verlag (1972). | MR | Zbl

[9] R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer Verlag, New York (1984). | MR | Zbl

[10] R. Glowinski and O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem. SIAM Rev. 21 (1979) 167-212. | MR | Zbl

[11] R. Glowinski and M. Wheeler, Domain decomposition and mixed finite element methods for elliptic problems, in Domain Decomposition Methods for Partial Differential Equations, SIAM (1988) 144-172. | MR | Zbl

[12] A.E. Green and W. Zerna, Theoretical Elasticity. Oxford University Press, 2nd. edn. (1968). | MR | Zbl

[13] W.T. Koiter, On the nonlinear theory of thin elastic shells, in Proc. Kon. Ned. Akad. Wetensch., Vol. B (1966) 1-54. | MR

[14] J.E. Lagnese, Boundary Stabilization of Thin Plates. SIAM, Philadelphia, Pennsylvania (1989). | MR | Zbl

[15] I. Lasiecka, Uniform stabilization of a full von Karman system with nonlinear boundary feedback. SIAM J. Control 36 (1998) 1376-1422. | MR | Zbl

[16] I. Lasiecka, Weak, classical and intermediate solutions to full von Karman system of dynamic nonlinear elasticity. Applicable Anal. 68 (1998) 123-145. | MR | Zbl

[17] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris (1969). | MR | Zbl

[18] J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer Verlag (1972). | Zbl

[19] L. Mansfield, Analysis of finite element methods for the nonlinear dynamic analysis of shells. Numerische Mathematik 42 (1983) 213-235. | MR | Zbl

[20] R. Marchand, Finite element approximations of control problems arising in nonlinear shell theory. Ph.D. thesis, University of Virginia (1996).

[21] V.G. Mazya and T.V. Shaposhnikova, Theory of Multipliers in Spaces of Differentiable Functions. Pitman (1985). | Zbl

[22] A. Raoult, Analyse mathématique de quelques modèles de plaques et de poutres élastiques ou élasto-plastiques. Doctoral Dissertation, Université Pierre et Marie Curie, Paris (1988).

[23] H.L. Royden, Real Analysis. Macmillan Publishing Company, 3rd edn. (1988). | MR | Zbl

[24] V.I. Sedenko, The uniqueness of generalized solutions of initial boundary value problem for Marguerre-Vlasov equation in the nonlinear oscillation theory of shallow shells. Izwestia Vysshyh Uchebnych Zavedenij (1994) 1-2.

[25] V. Thomee, Galerkin Finite Element Methods for Parabolic Problems. Springer Verlag (1984). | MR | Zbl