Comptes Rendus
no. 6
Numerical analysis
A simple nonconforming quadrilateral finite element
[Un élément fini non conforme quadrilatéral simple]

Présenté par : Olivier Pironneau

Boujemâa Achchab1 ; Abdellatif Agouzal2 ; Khalid Bouihat1
1 LM2CE, LAMSAD, Univ. Hassan 1
2 Université de Lyon, CNRS, Université Lyon-1, Institut Camille-Jordan, 69622 Villeurbanne cedex, France
Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 529-533.

Dans ce travail, nous présentons et analysons un élément fini non conforme en quadrangles. Nous obtenons une estimation d'erreur a priori optimale pour des quadrangles réguliers arbitraires. Nous présentons également l'idée d'extension tridimensionnelle de cet élément.

We introduce and analyze a simple nonconforming quadrilateral finite element and then we derive optimal a priori error estimates for arbitrary regular quadrilaterals. The idea of extension to some non-conforming elements for three-dimensional hexahedrons is also presented.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.03.020
Boujemâa Achchab 1 ; Abdellatif Agouzal 2 ; Khalid Bouihat 1

1 LM2CE, LAMSAD, Univ. Hassan 1
2 Université de Lyon, CNRS, Université Lyon-1, Institut Camille-Jordan, 69622 Villeurbanne cedex, France 
@article{CRMATH_2014__352_6_529_0,
     author = {Boujem\^aa Achchab and Abdellatif Agouzal and Khalid Bouihat},
     title = {A simple nonconforming quadrilateral finite element},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {529--533},
     publisher = {Elsevier},
     volume = {352},
     number = {6},
     year = {2014},
     doi = {10.1016/j.crma.2014.03.020},
     language = {en},
}
TY  - JOUR
AU  - Boujemâa Achchab
AU  - Abdellatif Agouzal
AU  - Khalid Bouihat
TI  - A simple nonconforming quadrilateral finite element
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 529
EP  - 533
VL  - 352
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2014.03.020
LA  - en
ID  - CRMATH_2014__352_6_529_0
ER  - 
%0 Journal Article
%A Boujemâa Achchab
%A Abdellatif Agouzal
%A Khalid Bouihat
%T A simple nonconforming quadrilateral finite element
%J Comptes Rendus. Mathématique
%D 2014
%P 529-533
%V 352
%N 6
%I Elsevier
%R 10.1016/j.crma.2014.03.020
%G en
%F CRMATH_2014__352_6_529_0
Boujemâa Achchab; Abdellatif Agouzal; Khalid Bouihat. A simple nonconforming quadrilateral finite element. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 529-533. doi : 10.1016/j.crma.2014.03.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.03.020/

[1] A. Agouzal A posteriori error estimators for nonconforming approximation, Int. J. Numer. Anal. Model., Volume 5 (2008) no. 1, pp. 77-85

[2] T. Arbogast; Zhangxin Chen On the implementation of mixed methods as nonconforming methods for second-order elliptic problems, Math. Comput., Volume 64 (1995) no. 211, pp. 943-972

[3] D.N. Arnold; D. Boffi; R.S. Falk Approximation by quadrilateral finite elements, Math. Comput., Volume 71 (2002), pp. 909-922

[4] M. Crouzeix; P.A. Raviart Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, ESAIM Math. Model. Numer. Anal., Volume 7 (1973) no. R3, pp. 33-75

[5] J. Douglas; J.E. Santos; D. Sheen; X. Ye Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, RAIRO Math. Model. Anal. Numer., Volume 33 (1999), pp. 747-770

[6] H. Han Nonconforming elements in the mixed finite element method, J. Comput. Math., Volume 2 (1984) no. 3, pp. 223-233

[7] H. Han A finite element approximation of Navier–Stokes equations using nonconforming elements, J. Comput. Math., Volume 2 (1984) no. 1, pp. 77-88

[8] V. Girault; P.-A. Raviart Finite Element Methods for Navier–Stokes Equations, Springer Verlag, 1986

[9] Jun Hu; Zhong-Ci Shi Constrained quadrilateral nonconforming rotated Q1-element, J. Comput. Math., Volume 23 (2005), pp. 561-586

[10] C. Park; D. Sheen P1-nonconforming quadrilateral finite element methods for second-order elliptic problems, SIAM J. Numer. Anal., Volume 41 (2003), pp. 624-640

[11] R. Rannacher; S. Turek Simple nonconforming quadrilateral Stokes element, Numer. Methods Partial Differ. Equ., Volume 8 (1992) no. 2, pp. 97-111

[12] Zhou Gang A class of arbitrarily convex quadrilateral elements for solving Navier–Stokes equations by nonconforming elements, Math. Numer. Sin., Volume 8 (1986) no. 3, pp. 258-274 (in Chinese)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations

Mingxia Li; Roland Becker; Shipeng Mao

C. R. Math (2011)