École Nationale Supérieure de
Techniques Avancées

Abstract

Here I present the Hybrid High Order method and its use for the numerical resolution of the acoustic wave equation. A thorough description of the HHO method is given in the context of the stationary diffusion problem. I also review the different possible time discretizations for the acoustic wave equation and offer a comparison of first and second order formulations. I then develop demonstrations of an estimation for the error in the energy- and the L 2 -norm, inspired by the stationary results and the Discontinuous Galerkin methodology. I finally compare these theoretical expectations to the numerical simulations of a Python generic code on a two-dimensional Cartesian mesh.