In this paper a penalized method and its approximation by finite element method are proposed to solve Koiter’s equations for a thin linearly elastic shell. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive some a priori error estimates. We are especially interested in the behavior of the solution when the penalty parameter goes to zero. We propose here a new formulation that leads to a quasi optimal and uniform error estimate with respect to the penalized parameter. In other words, we are able to show that this method converges uniformly with respect to the penalized parameter and to the mesh size. Numerical tests that validate and illustrate our approach are given.
Accepté le :
DOI : 10.1051/m2an/2017009
Mots clés : Shell theory, Koiter’s model, finite elements error analysis
@article{M2AN_2017__51_5_1783_0,
author = {Merabet, Ismail and Nicaise, Serge},
title = {A penalty method for a linear {Koiter} shell model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1783--1803},
publisher = {EDP-Sciences},
volume = {51},
number = {5},
year = {2017},
doi = {10.1051/m2an/2017009},
mrnumber = {3731549},
zbl = {1386.74089},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017009/}
}
TY - JOUR AU - Merabet, Ismail AU - Nicaise, Serge TI - A penalty method for a linear Koiter shell model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1783 EP - 1803 VL - 51 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017009/ DO - 10.1051/m2an/2017009 LA - en ID - M2AN_2017__51_5_1783_0 ER -
%0 Journal Article %A Merabet, Ismail %A Nicaise, Serge %T A penalty method for a linear Koiter shell model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1783-1803 %V 51 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017009/ %R 10.1051/m2an/2017009 %G en %F M2AN_2017__51_5_1783_0
Merabet, Ismail; Nicaise, Serge. A penalty method for a linear Koiter shell model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1783-1803. doi : 10.1051/m2an/2017009. http://www.numdam.org/articles/10.1051/m2an/2017009/
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