## Approximation of the controls for the beam equation with vanishing viscosity

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- by Ioan Florin Bugariu, Sorin Micu and Ionel Rovenţa PDF
- Math. Comp.
**85**(2016), 2259-2303 Request permission

## Abstract:

We consider a finite difference semi-discrete scheme for the approximation of the boundary controls of a 1-D equation modelling the transversal vibrations of a hinged beam. It is known that, due to the high frequency numerical spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural setting. Consequently, the convergence of the approximate boundary controls corresponding to initial data in the finite energy space cannot be guaranteed. We prove that, by adding a vanishing numerical viscosity, the uniform controllability property and the convergence of the scheme is ensured.## References

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## Additional Information

**Ioan Florin Bugariu**- Affiliation: Department of Mathematics, University of Craiova, 200585, Romania
- MR Author ID: 1056928
- Email: florin$_$bugariu$_$86@yahoo.com
**Sorin Micu**- Affiliation: Department of Mathematics, University of Craiova, 200585 and Institute of Mathematical Statistics and Applied Mathematics, 70700, Bucharest, Romania
- Email: sd$_$micu@yahoo.com
**Ionel Rovenţa**- Affiliation: Department of Mathematics, University of Craiova, 200585, Romania
- Email: ionelroventa@yahoo.com
- Received by editor(s): January 22, 2014
- Received by editor(s) in revised form: September 11, 2014, and January 6, 2015
- Published electronically: February 11, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp.
**85**(2016), 2259-2303 - MSC (2010): Primary 93B05, 58J45, 65N06, 30E05
- DOI: https://doi.org/10.1090/mcom/3064
- MathSciNet review: 3511282