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A mixed discontinuous finite element method for folded Naghdi's shell in Cartesian coordinates


Authors: S. Nicaise and I. Merabet
Journal: Math. Comp. 86 (2017), 1-47
MSC (2010): Primary 74K25; Secondary 65N30, 74S05
DOI: https://doi.org/10.1090/mcom/3094
Published electronically: March 3, 2016
MathSciNet review: 3557792
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Abstract: In this work a mixed method and its DG formulation are proposed to solve Naghdi's equations for a thin linearly elastic shell. The unknowns of the problem are the displacement of the points of the middle surface, the rotation field of the normal vector to the middle surface of the shell and a Lagrange multiplier which is introduced in order to enforce the tangency requirement on the rotation. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive an a priori error estimate. We further propose an a posteriori estimator that yields an upper bound and a lower bound of the error. Numerical tests that validate and illustrate our approach are given.


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Additional Information

S. Nicaise
Affiliation: LAMAV, Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes Cedex 9, France
Email: serge.nicaise@univ-valenciennes.fr

I. Merabet
Affiliation: Lab. LMA, Université de Ouargla, Ouargla 30000, Algérie
Email: merabet.ismail@univ-ouargla.dz

DOI: https://doi.org/10.1090/mcom/3094
Keywords: DG method, a posteriori analysis, Naghdi's shell
Received by editor(s): January 23, 2015
Received by editor(s) in revised form: June 19, 2015
Published electronically: March 3, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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