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The singular dynamic method for constrained second order hyperbolic equations: application to dynamic contact problems. (English) Zbl 1423.35240

Summary: 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.

MSC:

35L10 Second-order hyperbolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74M15 Contact in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
35L87 Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators

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