Analysis of Robust Hybridized Discontinuous Galerkin Methods for Viscoacoustic Wave Equations

Abstract In this paper we study hybridized discontinuous Galerkin methods for viscoacoustic wave equations with a general number of viscosity terms. For viscoacoustic equations rewritten as a first order symmetric hyperbolic system, we develop a hybridized local discontinuous Galerkin method which is robust for the number of viscosity terms. We show that the method satisfies a discrete energy estimate such that the implicit constants in the energy estimate are independent of the number of viscosity terms and the length of simulation time. Furthermore, we show that the sizes of reduced system after static condensation are independent of the number of viscosity terms. Optimal a priori error estimates with the Crank–Nicolson scheme are proved and numerical test results are included.