@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},
year = {2000},
publisher = {Dunod},
volume = {34},
number = {1},
mrnumber = {1735976},
zbl = {0965.74069},
language = {en},
url = {https://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 UR - https://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 %U https://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. https://www.numdam.org/item/M2AN_2000__34_1_63_0/
[1] , Méthodes d'Éléments Finis pour les Problèmes de Coques Minces. Masson, Paris-Milan-Barcelone (1994).
[2] and , 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. | Zbl | MR
[3] and , 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] , and , Existence theorems for two-dimensional linear shell theories. Technical Report 1771, Unité de Recherche INRIA-Rocquencourt (1992). | Zbl
[5] and , An existence theorem for a class of nonlinear shallow shell problems. J. Math. Pures Appl. 60 (1981) 285-308. | Zbl | MR
[6] , The Finite Element Method For Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978). | Zbl | MR
[7] and , Tangential differential equations for dynamical thin/shallow shells. J. Differential Equations 128 (1995) 125-167. | Zbl | MR
[8] , Tensor Analysis and Continuum Mechanics. Springer-Verlag (1972). | Zbl | MR
[9] , Numerical Methods for Nonlinear Variational Problems. Springer Verlag, New York (1984). | Zbl | MR
[10] and , Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem. SIAM Rev. 21 (1979) 167-212. | Zbl | MR
[11] and , Domain decomposition and mixed finite element methods for elliptic problems, in Domain Decomposition Methods for Partial Differential Equations, SIAM (1988) 144-172. | Zbl | MR
[12] and , Theoretical Elasticity. Oxford University Press, 2nd. edn. (1968). | Zbl | MR
[13] , On the nonlinear theory of thin elastic shells, in Proc. Kon. Ned. Akad. Wetensch., Vol. B (1966) 1-54. | MR
[14] , Boundary Stabilization of Thin Plates. SIAM, Philadelphia, Pennsylvania (1989). | Zbl | MR
[15] , Uniform stabilization of a full von Karman system with nonlinear boundary feedback. SIAM J. Control 36 (1998) 1376-1422. | Zbl | MR
[16] , Weak, classical and intermediate solutions to full von Karman system of dynamic nonlinear elasticity. Applicable Anal. 68 (1998) 123-145. | Zbl | MR
[17] , Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris (1969). | Zbl | MR
[18] and , Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer Verlag (1972). | Zbl
[19] , Analysis of finite element methods for the nonlinear dynamic analysis of shells. Numerische Mathematik 42 (1983) 213-235. | Zbl | MR
[20] , Finite element approximations of control problems arising in nonlinear shell theory. Ph.D. thesis, University of Virginia (1996).
[21] and , Theory of Multipliers in Spaces of Differentiable Functions. Pitman (1985). | Zbl
[22] , Analyse mathématique de quelques modèles de plaques et de poutres élastiques ou élasto-plastiques. Doctoral Dissertation, Université Pierre et Marie Curie, Paris (1988).
[23] , Real Analysis. Macmillan Publishing Company, 3rd edn. (1988). | Zbl | MR
[24] , 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] , Galerkin Finite Element Methods for Parabolic Problems. Springer Verlag (1984). | Zbl | MR






