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This paper deals with a one-dimensional wave equation being subjected to aunilateral boundary condition. An approximation of this problem combining thefinite element and mass redistribution methods is proposed. The massredistribution method is based on a redistribution of the body mass such thatthere is no inertia at the contact node and the mass of the contact node isredistributed on the other nodes. The convergence as well as an error estimatein time are proved. The analytical solution associated with a benchmark problemis introduced and it is compared to approximate solutions for different choicesof mass redistribution. However some oscillations for the energy associatedwith approximate solutions obtained for the second order schemes can beobserved after the impact. To overcome this difficulty, an new unconditionallystable and a very lightly dissipative scheme is proposed.

A weighted finite element mass redistribution method for dynamic contact problems