Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping
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| Format: | Preprint |
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2025
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| _version_ | 1866912304979771392 |
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| author | Gerbi, Stéphane Nasser, Rayan Wehbe, Ali |
| author_facet | Gerbi, Stéphane Nasser, Rayan Wehbe, Ali |
| contents | In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite Volume Method (FVM) and we are interested in deriving the stability estimates and the convergence of the numerical solution to the continuous one. Numerical experiments are performed to confirm the theoretical study on the decay rate of the solution to the null one when a localized damping acts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_19947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping Gerbi, Stéphane Nasser, Rayan Wehbe, Ali Analysis of PDEs Numerical Analysis In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite Volume Method (FVM) and we are interested in deriving the stability estimates and the convergence of the numerical solution to the continuous one. Numerical experiments are performed to confirm the theoretical study on the decay rate of the solution to the null one when a localized damping acts. |
| title | Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2502.19947 |