An energy-based discontinuous Galerkin method for the wave equation with advection
Numerical Analysis
2019-03-19 v1
Abstract
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both subsonic and supersonic advection is allowed. Error estimates in the energy norm are established, and numerical experiments on structured grids display optimal convergence in the norm for upwind fluxes. The method generalizes earlier work on energy-based discontinuous Galerkin methods for second order wave equations which was restricted to energy forms written as a simple sum of kinetic and potential energy.
Keywords
Cite
@article{arxiv.1903.06947,
title = {An energy-based discontinuous Galerkin method for the wave equation with advection},
author = {Lu Zhang and Thomas Hagstrom and Daniel Appelo},
journal= {arXiv preprint arXiv:1903.06947},
year = {2019}
}