English

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 L2L^2 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}
}