| Issue |
ESAIM: M2AN
Volume 51, Number 5, September-October 2017
|
|
|---|---|---|
| Page(s) | 1783 - 1803 | |
| DOI | https://doi.org/10.1051/m2an/2017009 | |
| Published online | 23 October 2017 | |
A penalty method for a linear Koiter shell model
1 LMA, Université Kasi Merbah – Ouargla, 30000, Algérie.
merabet.ismail@univ-ouargla.dz
2 LAMAV, Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes cedex 9, France.
serge.nicaise@univ-valenciennes.fr
Received: 22 April 2016
Accepted: 7 March 2017
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.
Mathematics Subject Classification: 74K25 / 65N30 / 74S05
Key words: Shell theory / Koiter’s model / finite elements error analysis
© EDP Sciences, SMAI 2017
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