Finite element methods on non-conforming grids by penalizing the matching constraint
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 357-372.

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

DOI : 10.1051/m2an:2003031
Classification : 65N12, 65N30, 65F10
Mots-clés : finite element methods, non-matching grids, penalty technique 
@article{M2AN_2003__37_2_357_0,
     author = {Boillat, Eric},
     title = {Finite element methods on non-conforming grids by penalizing the matching constraint},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {357--372},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     doi = {10.1051/m2an:2003031},
     mrnumber = {1991206},
     zbl = {1043.65124},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an:2003031/}
}
TY  - JOUR
AU  - Boillat, Eric
TI  - Finite element methods on non-conforming grids by penalizing the matching constraint
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2003
SP  - 357
EP  - 372
VL  - 37
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/m2an:2003031/
DO  - 10.1051/m2an:2003031
LA  - en
ID  - M2AN_2003__37_2_357_0
ER  - 
%0 Journal Article
%A Boillat, Eric
%T Finite element methods on non-conforming grids by penalizing the matching constraint
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2003
%P 357-372
%V 37
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/m2an:2003031/
%R 10.1051/m2an:2003031
%G en
%F M2AN_2003__37_2_357_0
Boillat, Eric. Finite element methods on non-conforming grids by penalizing the matching constraint. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 357-372. doi : 10.1051/m2an:2003031. http://archive.numdam.org/articles/10.1051/m2an:2003031/

[1] R.A. Adams, Sobolev Spaces. Academic Press, New-York, San Francisco, London (1975). | MR | Zbl

[2] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173-197. | Zbl

[3] F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér. 31 (1997) 289-302. | Numdam | Zbl

[4] M. Bercovier, Perturbation of mixed variational problems. Application to mixed finite element methods. RAIRO Anal. Numér. 12 (1978) 211-236. | Numdam | Zbl

[5] F. Brezzi and M. Fortin, Mixed and Hybride Finite Element Methods. Springer-Verlag, New York (1991). | MR | Zbl

[6] P.G. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland, Amsterdam (1978). | MR | Zbl

[7] P. Clement, Approximation by finite element using local regularization. RAIRO Ser. Rouge 8 (1975) 77-84. | Numdam | Zbl

[8] P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). | MR | Zbl

[9] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris (1968). | MR | Zbl

[10] Y. Maday, C. Bernardi and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Nonlinear Partial Differential Equations and their applications, H. Brezis and J.L. Lions Eds., Vol. XI, Pitman (1994) 13-51. | Zbl

[11] J. Nitsche, Über eine Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1970/1971) 9-15. | Zbl

[12] D. Schotzau, C. Schwab and R. Stenberg, Mixed hp-fem on anisotropic meshes ii. Hanging nodes and tensor products of boundary layer meshes. Numer. Math. 83 (1999) 667-697. | Zbl

[13] R. Stenberg, On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math. 63 (1995) 139-148. | Zbl

Cité par Sources :