Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction

David Doyen (1) , Alexandre Ern (2)

1 EDF - EDF
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

The aim of the present work is to analyze the modified mass method for the dynamic Signorini problem with Coulomb friction. We prove that the space semi-discrete problem is equivalent to an upper semi-continuous one-sided Lipschitz differential inclusion and is, therefore, well-posed. We derive an energy balance. Next, considering an implicit time-integration scheme, we prove that, under a certain condition on the discretization parameters, the fully discrete problem is well-posed. For a fixed discretization in space, we prove also that the fully discrete solutions converge to the space semi-discrete solution when the time step tends to zero.

Mots clés: Finite elements; Time-integration scheme; Elastodynamics; Unilateral contact; Coulomb friction; Differential inclusion; Modified mass method

Domaines: Analyse numérique [math.NA]

David Doyen, Alexandre Ern. Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction. SIAM Journal on Numerical Analysis, 2011, 49 (5), pp.2039-2056. ⟨10.1137/100804711⟩. ⟨hal-00473809⟩