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Quadratic finite elements with non-matching grids for the unilateral boundary contact

Published online by Cambridge University Press:  17 June 2013

S. Auliac ,
Z. Belhachmi ,
F. Ben Belgacem  and
F. Hecht
S. Auliac
Affiliation:
LJLL, C.N.R.S. Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France.. auliac@ann.jussieu.fr
Z. Belhachmi
Affiliation:
LMIA, EA CNRS, Université deq Haute Alsace, Rue des Frères Lumière, 68096 Mulhouse, France.; zakaria.belhachmi@uha.fr
F. Ben Belgacem
Affiliation:
LMAC, EA 2222, Université de Technologie de Compiègne, BP 20529, 60205 Compiègne Cedex, France.; faker.ben-belgacem@utc.fr I2M (UMR CNRS 5295), Site ENSCBP, 16 Avenue Pey Berland, 33607 Pessac Cedex, France.
F. Hecht
Affiliation:
LJLL, C.N.R.S. Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France.; hecht@ann.jussieu.fr
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Abstract

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.

Keywords

Unilateral contact conditionsquadratic finite elementsnon-matching gridsmortar matching
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 1185 - 1205
Copyright
© EDP Sciences, SMAI, 2013

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