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: existence, uniqueness, convergence, mass redistribution method, variational inequality, unilateral contact
@article{M2AN_2014__48_4_1147_0,
author = {Dabaghi, Farshid and Petrov, Adrien and Pousin, J\'er\^ome and Renard, Yves},
title = {Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1147--1169},
year = {2014},
publisher = {EDP Sciences},
volume = {48},
number = {4},
doi = {10.1051/m2an/2013133},
mrnumber = {3264349},
zbl = {1297.35148},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2013133/}
}
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 PY - 2014 SP - 1147 EP - 1169 VL - 48 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2013133/ DO - 10.1051/m2an/2013133 LA - en ID - M2AN_2014__48_4_1147_0 ER -
%0 Journal Article %A Dabaghi, Farshid %A Petrov, Adrien %A Pousin, Jérôme %A Renard, Yves %T Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1147-1169 %V 48 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2013133/ %R 10.1051/m2an/2013133 %G en %F M2AN_2014__48_4_1147_0
Dabaghi, Farshid; Petrov, Adrien; Pousin, Jérôme; Renard, Yves. Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1147-1169. doi: 10.1051/m2an/2013133
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