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

Authors:
Yves Renard
Affiliations:
Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, F-69621, Villeurbanne, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.