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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Renard, Yves

关键词: Hyperbolic partial differential equation;    Constrained equation;    Finite element methods;    Variational inequalities;   

DOI  :  10.1016/j.cam.2010.01.058

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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