Numerical approximation of a wave equation with unilateral constraints
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 by Michelle Schatzman and Michel Bercovier PDF
 Math. Comp. 53 (1989), 5579 Request permission
Abstract:
The system ${u_{tt}}  {u_{xx}} \backepsilon f$, $x \in (0,L) \times (0,T)$, with initial data $u(x,0) = {u_0}(x)$, ${u_t}(x,0) = {u_1}(x)$ almost everywhere on (0, L) and boundary conditions $u(0,t) = 0$, for all $t \geq 0$, and the unilateral condition \[ {u_x}(L,t) \geq 0,u(L,t) \geq {k_0},(u(L,t)  {k_0}){u_x}(L,t) = 0\] models the longitudinal vibrations of a rod, whose motion is limited by a rigid obstacle at one end. A new variational formulation is given; existence and uniqueness are proved. Finite elements and finite difference schemes are given, and their convergence is proved. Numerical experiments are reported; the characteristic schemes perform better in terms of accuracy, and the subcharacteristic schemes look better.References

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Additional Information
 © Copyright 1989 American Mathematical Society
 Journal: Math. Comp. 53 (1989), 5579
 MSC: Primary 65M25; Secondary 65N30
 DOI: https://doi.org/10.1090/S00255718198909694915
 MathSciNet review: 969491