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Article Dans Une Revue Mathematics of Computation Année : 2019

Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using finite-difference method

Résumé

We consider a finite-differences semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation. The high frequency numerical spurious oscillations lead to a loss of the uniform (with respect to the mesh-size) controllability property of the semi-discrete model in the natural setting. We prove that, by filtering the high frequencies of the initial data in an optimal range, we restore the uniform controllability property. Moreover, we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability.
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Dates et versions

hal-01338619 , version 1 (28-06-2016)
hal-01338619 , version 2 (15-04-2018)

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  • HAL Id : hal-01338619 , version 2

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Pierre Lissy, Ionel Roventa. Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using finite-difference method. Mathematics of Computation, 2019, 88. ⟨hal-01338619v2⟩
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