Geodesic
A penalty method for a linear Koiter shell model
Merabet, Ismail1 ; Nicaise, Serge2 
1 LMA, Université Kasi Merbah – Ouargla, 30000, Algérie.
2 LAMAV, Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes cedex 9, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1783-1803

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017009
Classification : 74K25, 65N30, 74S05
Keywords: Shell theory, Koiter’s model, finite elements error analysis

Merabet, Ismail 1 ; Nicaise, Serge 2

1 LMA, Université Kasi Merbah – Ouargla, 30000, Algérie.
2 LAMAV, Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes cedex 9, France. 
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     title = {A penalty method for a linear {Koiter} shell model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1783--1803},
     publisher = {EDP-Sciences},
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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

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