| Volume 3, Number 2, 2013, Pages 169-182 DOI：10.11948/2013013 |
| Numerical analysis for a locally damped wave equation |
| Mauro Antonio Rincon,Maria Inês Martins Copetti |
| Keywords:Damped wave equation |
| Abstract: |
| We consider a semi-discrete finite element formulation with artificial viscosity for the numerical approximation of a problem that models the damped vibrations of a string with fixed ends. The damping coefficient depends on the spatial variable and is effective only in a sub-interval of the domain. For this scheme, the energy of semi-discrete solutions decays exponentially and uniformly with respect to the mesh parameter to zero. We also introduce an implicit in time discretization. Error estimates for the semi-discrete and fully discrete schemes in the energy norm are provided and numerical experiments performed. |
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