Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping
Provides a rigorous numerical analysis for a specific class of wave equations with non-smooth coefficients and localized damping, which is incremental for researchers in numerical PDEs.
The paper develops a finite volume method for a 1-D wave equation with non-smooth wave speed and localized Kelvin-Voigt damping, proving stability and convergence. Numerical experiments confirm the theoretical decay rate of the solution to zero under localized damping.
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.