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

Farshid Dabaghi; Adrien Petrov; Jérôme Pousin; Yves Renard

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 4, page 1147-1169
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Dabaghi, Farshid, et al. "Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 1147-1169. <http://eudml.org/doc/273163>.

@article{Dabaghi2014,
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.},
author = {Dabaghi, Farshid, Petrov, Adrien, Pousin, Jérôme, Renard, Yves},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {existence; uniqueness; convergence; mass redistribution method; variational inequality; unilateral contact; numerical experiments},
language = {eng},
number = {4},
pages = {1147-1169},
publisher = {EDP-Sciences},
title = {Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary},
url = {http://eudml.org/doc/273163},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Dabaghi, Farshid
AU - Petrov, Adrien
AU - Pousin, Jérôme
AU - Renard, Yves
TI - Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 4
SP - 1147
EP - 1169
AB - 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.
LA - eng
KW - existence; uniqueness; convergence; mass redistribution method; variational inequality; unilateral contact; numerical experiments
UR - http://eudml.org/doc/273163
ER -

References

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