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, Volume 48 (2014) no. 4, p. 1147-1169
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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.

DOI : https://doi.org/10.1051/m2an/2013133
Classification:  35L85,  35L05,  65N30,  74M15
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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     pages = {1147-1169},
     doi = {10.1051/m2an/2013133},
     zbl = {1297.35148},
     mrnumber = {3264349},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 4, pp. 1147-1169. doi : 10.1051/m2an/2013133. http://www.numdam.org/item/M2AN_2014__48_4_1147_0/

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