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A posteriori analysis of finite element discretizations

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Niveau: Supérieur, Doctorat, Bac+8
A posteriori analysis of finite element discretizations of a Naghdi shell model by Christine Bernardi1, Adel Blouza2, Frederic Hecht1, and Herve Le Dret1 Abstract: We consider two finite element discretizations of the Naghdi equations which model a thin three-dimensional shell. Both of them are derived from a mixed formulation of these equations, and a penalty term is added in the second one. The a posteriori analysis of the discrete problems leads to the construction of error indicators which satisfy optimal estimates. We describe a mesh adaptivity strategy relying on these indicators and we present some numerical experiments that confirm its efficiency. Resume: Nous considerons deux discretisations par elements finis des equations de Naghdi qui modelisent une coque tridimensionnelle de faible epaisseur. Les deux problemes discrets sont construits a partir d'une formulation mixte de ces equations, avec un terme de penalisation supplementaire dans le second. L'analyse a posteriori de ces problemes mene a la construction d'indicateurs d'erreur qui satisfont des estimations optimales. Nous proposons une strategie d'adaptation de maillage basee sur ces indicateurs et presentons quelques experiences numeriques qui confirment son efficacite. 1 Universite Pierre et Marie Curie-Paris6, UMR 7598 LJLL, Paris, F-75005 France; CNRS, UMR 7598 LJLL, Paris, F-75005 France. 2 Laboratoire de Mathematiques Raphael Salem (UMR 6085 CNRS), Universite de Rouen, avenue de l'Universite, B.

  • a? ·

  • elasticity tensor

  • model linearly

  • saddle-point problems

  • final mesh

  • strategie d'adaptation de maillage basee

  • argyris triangles provide

  • dimensional shell


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Language English
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A
posteriori
analysis
of a
of finite element discretizations
Naghdi shell model
by Christine Bernardi1, Adel Blouza2r´,FcHri´eedthce1Deertna,Le´vreHd1
Abstract:two finite element discretizations of the Naghdi equations whichWe consider model a thin three-dimensional shell. Both of them are derived from a mixed formulation of these equations, and a penalty term is added in the second one. The a posteriori analysis of the discrete problems leads to the construction of error indicators which satisfy optimal estimates. We describe a mesh adaptivity strategy relying on these indicators and we present some numerical experiments that confirm its efficiency.
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1rsitniveUirCeteaMreere´iPR7UM6,isar-Pieur-F,siraP,LLJL8955700F5arcn;e CNRS, UMR 7598 LJLL, Paris, F-75005 France. 2metata´hRspaqieulSalha¨eMR60em(U,)SRNC58isrevinUoueRedt´,enLaraboirtoeMed ´ avenuedelUniversit´e,B.P.12,F-76801Saint-Etienne-du-Rouvray,France. e-mail addresses: bernardi@ann.jussieu.fr, Adel.Blouza@univ-rouen.fr, hecht@ann.jussieu.fr, ledret@ann.jussieu.fr