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Journal Articles Journal of Computational and Applied Mathematics Year : 2010

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

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.
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hal-01461799 , version 1 (08-02-2017)

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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⟩
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