HP a-priori error estimates for a non-dissipative spectral discontinuous Galerkin method to solve the Maxwell equations in the time domain

In this paper, we present the hp-convergence analysis of a nondissipative high-order discontinuous Galerkin method on unstructured hexahedral meshes using a mass-lumping technique to solve the time-dependent Maxwell equations. In particular, we underline the spectral convergence of the method (in the sense that when the solutions and the data are very smooth, the discretization is of unlimited order). Moreover, we see that the choice of a non-standard approximate space (for a discontinuous formulation) with the absence of dissipation can imply a loss of spatial convergence. Finally we present a numerical result which seems to confirm this property.