Geodesic
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

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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 : 10.1051/m2an/2013133
Classification : 35L85, 35L05, 65N30, 74M15
Keywords: existence, uniqueness, convergence, mass redistribution method, variational inequality, unilateral contact 
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     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},
     publisher = {EDP-Sciences},
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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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