Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods

A numerical approximation of the acoustic wave equation is presented. The spatial discretization is based on conforming spectral elements, whereas we use finite difference Newmark's explicit integration schemes for the temporal discretization. A rigorous stability analysis is developed for the discretized problem providing an upper bound for the time step At. We present several numerical results concerning stability and convergence properties of the proposed numerical methods.