On the convergence of a shock capturing discontinuous Galerkin method for nonlinear hyperbolic systems of conservation laws
Abstract
In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entropy variables using an entropy stable numerical flux. While being similar to the method proposed in [14], our approach is new in that we do not use streamline diffusion (SD) stabilization. It is proved that an artificial-viscosity-based nonlinear shock capturing mechanism is sufficient to ensure both entropy stability and entropy consistency, and consequently we establish convergence to an entropy measure-valued (emv) solution. The result is valid for general systems and arbitrary order discontinuous Galerkin method.
Keywords
Cite
@article{arxiv.1404.6030,
title = {On the convergence of a shock capturing discontinuous Galerkin method for nonlinear hyperbolic systems of conservation laws},
author = {Mohammad Zakerzadeh and Georg May},
journal= {arXiv preprint arXiv:1404.6030},
year = {2016}
}
Comments
Comments: Affiliations added Comments: Numerical results added, shortened proof