The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems

Yves Renard (1, 2)

1 ICJ - Institut Camille Jordan
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The main application is dynamic contact problems. The principle consists in the use of a singular mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. We prove that the semi-discretized problem is well-posed and energy conserving. Numerical experiments show that this is a crucial property to build stable numerical schemes.

Mots clés: hyperbolic partial differential equation; constrained equation; finite element; methods; variational inequalities

Domaines: Mécanique [physics.med-ph]

Yves Renard. The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems. Journal of Computational and Applied Mathematics, 2010, 234, pp.906-923. ⟨10.1016/j.cam.2010.01.058⟩. ⟨hal-01461799⟩