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Numerical approximation of a wave equation with unilateral constraints. (English) Zbl 0683.65088
An initial-boundary-value problem is considered for the one-dimensional wave equation by way of the example of longitudinal vibrations of a rod. A Dirichlet boundary condition is assumed at one end, while a unilateral condition is given at the second end. A variational formulation of the problem is presented and existence as well as uniqueness of the solution are proved.
Finite elements and finite difference schemes are developed and their convergence is discussed. Numerical experiments are carried out making use of finite difference schemes, either characteristic or subcharacteristics, with initial data which are differentiable or not differentiable functions. The authors’ conclusion is that the characteristic scheme gives very good results and the subcharacteristic scheme gives worse results, even if they look smoother.
Reviewer: Z.Dżygadło

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35L05 Wave equation
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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