A posteriori analysis of a finite element discretization of a Naghdi shell model

被引:6
作者
Bernardi, Christine [1 ,2 ]
Hecht, Frederic [1 ,2 ]
Le Dret, Herve [1 ,2 ]
Blouza, Adel [3 ]
机构
[1] CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France
[2] Univ Paris 06, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France
[3] Univ Rouen, Lab Math Raphael Salem, UMR 6085, CNRS, F-76801 St Etienne, France
关键词
Naghdi shell model; finite elements; a posteriori analysis; ERROR ESTIMATION; PLATE; APPROXIMATION; UNIQUENESS; EXISTENCE; LOCKING;
D O I
10.1093/imanum/drs009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We are interested in the finite element discretization of the Naghdi equations, which model a thin three-dimensional shell. The discrete problem is derived from a mixed formulation of these equations. Its a posteriori analysis 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.
引用
收藏
页码:190 / 211
页数:22
相关论文
共 29 条
[1]  
[Anonymous], 2003, CO FL SO ME
[2]   Locking-free finite element methods for shells [J].
Arnold, DN ;
Brezzi, F .
MATHEMATICS OF COMPUTATION, 1997, 66 (217) :1-14
[3]  
BERNADOU M., 1994, COLLECTION RECHERCHE, V33
[4]  
BERNADOU M, 1976, LECTURE NOTES EC MAT, V134, P89, DOI DOI 10.1007/978-3-642-85972-4_7
[5]   Spectral discretization of a Naghdi shell model [J].
Bernard, Christine ;
Blouza, Adel .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (06) :2653-2670
[6]   A posteriori analysis of a penalty method and application to the stokes problem [J].
Bernardi, C ;
Girault, V ;
Hecht, F .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2003, 13 (11) :1599-1628
[7]  
Bernardi C., DISCRETISATIONS VARI, V45
[8]   Existence and uniqueness for the linear Koiter model for shells with little regularity [J].
Blouza, A ;
Le Dret, H .
QUARTERLY OF APPLIED MATHEMATICS, 1999, 57 (02) :317-337
[9]   Nagdhi's shell model: Existence, uniqueness and continuous dependence on the midsurface [J].
Blouza, A ;
Le Dret, H .
JOURNAL OF ELASTICITY, 2001, 64 (2-3) :199-216
[10]   Two finite element approximations of Naghdi's shell model in Cartesian coordinates [J].
Blouza, Adel ;
Hecht, Frederic ;
Le Dret, Herve .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (02) :636-654