UNIFORM-IN-TIME SUPERCONVERGENCE OF THE HDG METHODS FOR THE ACOUSTIC WAVE EQUATION

We present the first a priori error analysis of the hybridizable discontinuous Galerkin methods for the acoustic equation in the time-continuous case. We show that the velocity and the gradient converge with the optimal order of k + 1 in the L-2-norm uniformly in time whenever polynomials of degree k >= 0 are used. Finally, we show how to take advantage of this local postprocessing to obtain an approximation to the original scalar unknown also converging with order k + 2 for k >= 1. This puts on firm mathematical ground the numerical results obtained in J. Comput. Phys. 230 (2011), 3695-3718.