Some Abstract Error Estimates of a Finite Volume Scheme for the Wave Equation on General Nonconforming Multidimensional Spatial Meshes

A general class of nonconforming meshes has been recently studied for sationary anisotropic heterogeneous diffusion problems, see [2]. The aim of this contribution is to deal with error estimates, using this new class of meshes, for the wave equation. We present an implicit time scheme to approximate the wave equation. We prove that, when the discrete flux is calculated using a stabilized discrete gradient, the convergence order is h(D) + k, where h(D) (resp. k) is the mesh size of the spatial (resp. time) discretization. This estimate is valid for discrete norms L-infinity(0, T; H-0(1)(ohm)) and W-1.infinity(0, T; L-2(ohm)) under the regularity assumption u is an element of C-3([0, T]; C-2(ohm)) for the exact solution u. These error estimates are useful because they allow to obtain approximations to the exact solution and its first derivatives of order h(D) + k.