Stable Spectral-Volume Methods
Numerical Analysis
2025-02-12 v1 Numerical Analysis
Abstract
A novel approach for the stabilization of the Spectral-Volume (SV) method based on Dafermos' entropy rate criterion is presented. The method is an adaption of an already existing approach for the stabilization of the Discontinuous-Galerkin (DG) method. It employs the same estimates for the maximal possible entropy dissipation rate as the DG version. However, a new way to compute the discrete conservative filter had to be derived due to the differences of the underlying schemes. The resulting modified SV scheme even satisfies the entropy inequality. Tests are carried out for Burgers' equation and for the Euler equations of gas dynamics.
Keywords
Cite
@article{arxiv.2502.07055,
title = {Stable Spectral-Volume Methods},
author = {Lena Schadt},
journal= {arXiv preprint arXiv:2502.07055},
year = {2025}
}
Comments
40 pages, 16 figures, submitted to Foundations of Computational Mathematics