Comptes Rendus
Partial Differential Equations/Numerical Analysis
Approximation of the biharmonic problem using piecewise linear finite elements
[Approximation d'un problème biharmonique par élément fini P1]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1283-1286.

Nous proposons une approximation de la solution du problème bi-harmonique dans H02(Ω) basée sur la discrétisation du Laplacien par éléments finis P1 continus mais non conformes.

We propose an approximation of the solution of the biharmonic problem in H02(Ω) which relies on the discretization of the Laplace operator using nonconforming continuous piecewise linear finite elements.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.11.002

Robert Eymard 1 ; Raphaèle Herbin 2

1 Laboratoire d'analyse et de mathématiques appliquées, UMR CNRS 8050, Université Paris-Est, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
2 Laboratoire d'analyse, topologie et probabilités, UMR CNRS 6632, Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France
@article{CRMATH_2010__348_23-24_1283_0,
     author = {Robert Eymard and Rapha\`ele Herbin},
     title = {Approximation of the biharmonic problem using piecewise linear finite elements},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1283--1286},
     publisher = {Elsevier},
     volume = {348},
     number = {23-24},
     year = {2010},
     doi = {10.1016/j.crma.2010.11.002},
     language = {en},
}
TY  - JOUR
AU  - Robert Eymard
AU  - Raphaèle Herbin
TI  - Approximation of the biharmonic problem using piecewise linear finite elements
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1283
EP  - 1286
VL  - 348
IS  - 23-24
PB  - Elsevier
DO  - 10.1016/j.crma.2010.11.002
LA  - en
ID  - CRMATH_2010__348_23-24_1283_0
ER  - 
%0 Journal Article
%A Robert Eymard
%A Raphaèle Herbin
%T Approximation of the biharmonic problem using piecewise linear finite elements
%J Comptes Rendus. Mathématique
%D 2010
%P 1283-1286
%V 348
%N 23-24
%I Elsevier
%R 10.1016/j.crma.2010.11.002
%G en
%F CRMATH_2010__348_23-24_1283_0
Robert Eymard; Raphaèle Herbin. Approximation of the biharmonic problem using piecewise linear finite elements. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1283-1286. doi : 10.1016/j.crma.2010.11.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.002/

[1] M. Ben-Artzi; I. Chorev; J.-P. Croisille; D. Fishelov A compact difference scheme for the biharmonic equation in planar irregular domains, SIAM J. Numer. Anal., Volume 47 (2009) no. 4, pp. 3087-3108

[2] M. Ben-Artzi; J.-P. Croisille; D. Fishelov A fast direct solver for the biharmonic problem in a rectangular grid, SIAM J. Sci. Comput., Volume 31 (2008) no. 1, pp. 303-333

[3] C. Bi; L. Li Mortar finite volume method with Adini element for biharmonic problem, J. Comput. Math., Volume 22 (2004) no. 3, pp. 475-488

[4] S.C. Brenner; L.-Y. Sung C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains, J. Sci. Comput., Volume 22/23 (2005), pp. 83-118

[5] F. Brezzi; M. Fortin Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991

[6] G. Chen; Z. Li; P. Lin A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow, Adv. Comput. Math., Volume 29 (2008) no. 2, pp. 113-133

[7] P.G. Ciarlet The finite element method (P.G. Ciarlet; J.-L. Lions, eds.), Handbook of Numerical Analysis, vol. III, Part I, North-Holland, Amsterdam, 1991

[8] P. Destuynder; M. Salaun Mathematical Analysis of Thin Plate Models, Mathématiques & Applications [Mathematics & Applications], vol. 24, Springer-Verlag, Berlin, 1996

[9] R. Eymard, T. Gallouët, Herbin, Finite volume schemes for the biharmonic problem on general meshes, 2010, submitted for publication.

[10] E.H. Georgoulis; P. Houston Discontinuous Galerkin methods for the biharmonic problem, IMA J. Numer. Anal., Volume 29 (2009) no. 3, pp. 573-594

[11] T. Gudi; N. Nataraj; A.K. Pani Mixed discontinuous Galerkin finite element method for the biharmonic equation, J. Sci. Comput., Volume 37 (2008) no. 2, pp. 139-161

[12] I. Mozolevski; E. Süli; P.R. Bösing hp-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation, J. Sci. Comput., Volume 30 (2007) no. 3, pp. 465-491

[13] E. Süli; I. Mozolevski hp-version interior penalty DGFEMs for the biharmonic equation, Comput. Methods Appl. Mech. Engrg., Volume 196 (2007) no. 13–16, pp. 1851-1863

[14] T. Wang A mixed finite volume element method based on rectangular mesh for biharmonic equations, J. Comput. Appl. Math., Volume 172 (2004) no. 1, pp. 117-130

Cité par Sources :

Commentaires - Politique