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We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper accuracy of the quadratic finite elements. This approach has already been used and proved to be reliable for the unilateral contact problems even for large deformations. We provide however some numerical examples to support the theoretical predictions.
@article{M2AN_2013__47_4_1185_0,
author = {Auliac, S. and Belhachmi, Z. and Ben Belgacem, F. and Hecht, F.},
title = {Quadratic finite elements with non-matching grids for the unilateral boundary contact},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1185--1205},
publisher = {EDP-Sciences},
volume = {47},
number = {4},
year = {2013},
doi = {10.1051/m2an/2012064},
mrnumber = {3082294},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012064/}
}
TY - JOUR AU - Auliac, S. AU - Belhachmi, Z. AU - Ben Belgacem, F. AU - Hecht, F. TI - Quadratic finite elements with non-matching grids for the unilateral boundary contact JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1185 EP - 1205 VL - 47 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012064/ DO - 10.1051/m2an/2012064 LA - en ID - M2AN_2013__47_4_1185_0 ER -
%0 Journal Article %A Auliac, S. %A Belhachmi, Z. %A Ben Belgacem, F. %A Hecht, F. %T Quadratic finite elements with non-matching grids for the unilateral boundary contact %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1185-1205 %V 47 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012064/ %R 10.1051/m2an/2012064 %G en %F M2AN_2013__47_4_1185_0
Auliac, S.; Belhachmi, Z.; Ben Belgacem, F.; Hecht, F. Quadratic finite elements with non-matching grids for the unilateral boundary contact. ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1185-1205. doi: 10.1051/m2an/2012064
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