Authors:	Hillebrand, Dorian Klein, Simon-Christian Öffner, Philipp
Title:	Applications of limiters, neural networks and polynomial annihilation in higher-order FD/FV schemes
Online publication date:	5-Jan-2024
Year of first publication:	2023
Language:	english
Abstract:	The construction of high-order structure-preserving numerical schemes to solve hyperbolic conservation laws has attracted a lot of attention in the last decades and various different ansatzes exist. In this paper, we compare several completely different approaches, i.e. deep neural networks, limiters and the application of polynomial annihilation to construct high-order accurate shock capturing finite difference/volume (FD/FV) schemes. We further analyze their analytical and numerical properties. We demonstrate that all techniques can be used and yield highly efficient FD/FV methods but also come with some additional drawbacks which we point out. Our investigation of the different strategies should lead to a better understanding of those techniques and can be transferred to other numerical methods as well which use similar ideas.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-9856
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Journal of scientific computing 97
Pages or article number:	13
Publisher:	Springer Science + Business Media B.V.
Publisher place:	New York, NY [u.a.]
Issue date:	2023
ISSN:	1573-7691
Publisher DOI:	10.1007/s10915-023-02322-2
Appears in collections:	DFG-491381577-H