Stabilizing Discontinuous Galerkin Methods Using Dafermos' Entropy Rate Criterion: II -- Systems of Conservation Laws and Entropy Inequality Predictors
Numerical Analysis
2023-06-09 v1 Numerical Analysis
Analysis of PDEs
Abstract
A novel approach for the stabilization of the Discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. First, estimates for the maximal possible entropy dissipation rate of a weak solution are derived. Second, families of conservative Hilbert-Schmidt operators are identified to dissipate entropy. Steering these operators using the bounds on the entropy dissipation results in high-order accurate shock-capturing DG schemes for the Euler equations, satisfying the entropy rate criterion and an entropy inequality.
Keywords
Cite
@article{arxiv.2306.05124,
title = {Stabilizing Discontinuous Galerkin Methods Using Dafermos' Entropy Rate Criterion: II -- Systems of Conservation Laws and Entropy Inequality Predictors},
author = {Simon-Christian Klein},
journal= {arXiv preprint arXiv:2306.05124},
year = {2023}
}