In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
Mots clés : Nitsche's method, overlapping grids
@article{M2AN_2003__37_3_495_0,
author = {Hansbo, Anita and Hansbo, Peter and Larson, Mats G.},
title = {A finite element method on composite grids based on {Nitsche's} method},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {495--514},
publisher = {EDP-Sciences},
volume = {37},
number = {3},
year = {2003},
doi = {10.1051/m2an:2003039},
zbl = {1031.65128},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003039/}
}
TY - JOUR AU - Hansbo, Anita AU - Hansbo, Peter AU - Larson, Mats G. TI - A finite element method on composite grids based on Nitsche's method JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 495 EP - 514 VL - 37 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003039/ DO - 10.1051/m2an:2003039 LA - en ID - M2AN_2003__37_3_495_0 ER -
%0 Journal Article %A Hansbo, Anita %A Hansbo, Peter %A Larson, Mats G. %T A finite element method on composite grids based on Nitsche's method %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 495-514 %V 37 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003039/ %R 10.1051/m2an:2003039 %G en %F M2AN_2003__37_3_495_0
Hansbo, Anita; Hansbo, Peter; Larson, Mats G. A finite element method on composite grids based on Nitsche's method. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 3, pp. 495-514. doi : 10.1051/m2an:2003039. http://archive.numdam.org/articles/10.1051/m2an:2003039/
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