Numerical approximation of acoustic waves by spectral element methods

In this paper we consider the approximation of acoustic wave propagation problems. Precisely, we investigate the stability and convergence of the classical Newmark schema in time and spectral element discretization in space for the wave problems. A special attention is payed to the non-homogeneous boundary data. Some detailed error estimates are obtained. From these results, the spectral accuracy and influences of the non-homogeneous boundary data are made evident. Several numerical examples are provided to confirm our theoretical analysis. The advantage of the present method is demonstrated by a numerical comparison with the finite element method.