| Issue |
ESAIM: M2AN
Volume 48, Number 4, July-August 2014
|
|
|---|---|---|
| Page(s) | 1147 - 1169 | |
| DOI | https://doi.org/10.1051/m2an/2013133 | |
| Published online | 08 July 2014 | |
Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary
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
Received:
23
January
2013
Revised:
11
June
2013
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.
Mathematics Subject Classification: 35L85 / 35L05 / 65N30 / 74M15
Key words: Existence / uniqueness / convergence / mass redistribution method / variational inequality / unilateral contact
© EDP Sciences, SMAI 2014
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