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Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary

Published online by Cambridge University Press:  08 July 2014

Farshid Dabaghi ,
Adrien Petrov ,
Jérôme Pousin  and
Yves Renard
Farshid Dabaghi
Affiliation:
Universitéde Lyon, CNRS, INSA-Lyon, Institut Camille Jordan UMR 5208, 20 Avenue A. Einstein, 69621 Villeurbanne, France. . farshid.dabaghi@insa-lyon.fr; apetrov@math.univ-lyon1.fr jerome.pousin@insa-lyon.fr; Yves.Renard@insa-lyon.fr
Adrien Petrov
Affiliation:
Universitéde Lyon, CNRS, INSA-Lyon, Institut Camille Jordan UMR 5208, 20 Avenue A. Einstein, 69621 Villeurbanne, France. . farshid.dabaghi@insa-lyon.fr; apetrov@math.univ-lyon1.fr jerome.pousin@insa-lyon.fr; Yves.Renard@insa-lyon.fr
Jérôme Pousin
Affiliation:
Universitéde Lyon, CNRS, INSA-Lyon, Institut Camille Jordan UMR 5208, 20 Avenue A. Einstein, 69621 Villeurbanne, France. . farshid.dabaghi@insa-lyon.fr; apetrov@math.univ-lyon1.fr jerome.pousin@insa-lyon.fr; Yves.Renard@insa-lyon.fr
Yves Renard
Affiliation:
Universitéde Lyon, CNRS, INSA-Lyon, Institut Camille Jordan UMR 5208, 20 Avenue A. Einstein, 69621 Villeurbanne, France. . farshid.dabaghi@insa-lyon.fr; apetrov@math.univ-lyon1.fr jerome.pousin@insa-lyon.fr; Yves.Renard@insa-lyon.fr
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Abstract

This paper focuses on a one-dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method, which is based on a redistribution of the body mass such that there is no inertia at the contact node, is introduced and its convergence is proved. Finally, some numerical experiments are reported.

Keywords

Existenceuniquenessconvergencemass redistribution methodvariational inequalityunilateral contact
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 4 , July 2014 , pp. 1147 - 1169
Copyright
© EDP Sciences, SMAI 2014

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