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.
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://www.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://www.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://www.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://www.numdam.org/articles/10.1051/m2an:2003031/
[1] , Sobolev Spaces. Academic Press, New-York, San Francisco, London (1975). | MR | Zbl
[2] , The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173-197. | Zbl
[3] and, The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér. 31 (1997) 289-302. | Numdam | Zbl
[4] , Perturbation of mixed variational problems. Application to mixed finite element methods. RAIRO Anal. Numér. 12 (1978) 211-236. | Numdam | Zbl
[5] and, Mixed and Hybride Finite Element Methods. Springer-Verlag, New York (1991). | MR | Zbl
[6] , The Finite Element Method for Elliptic Problem. North Holland, Amsterdam (1978). | MR | Zbl
[7] , Approximation by finite element using local regularization. RAIRO Ser. Rouge 8 (1975) 77-84. | Numdam | Zbl
[8] , Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). | MR | Zbl
[9] and, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris (1968). | MR | Zbl
[10] , and, 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] , 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] , and, Mixed hp-fem on anisotropic meshes ii. Hanging nodes and tensor products of boundary layer meshes. Numer. Math. 83 (1999) 667-697. | Zbl
[13] , On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math. 63 (1995) 139-148. | Zbl
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