Autoren:	Hillebrand, Dorian Klein, Simon-Christian Öffner, Philipp
Titel:	Applications of limiters, neural networks and polynomial annihilation in higher-order FD/FV schemes
Online-Publikationsdatum:	5-Jan-2024
Erscheinungsdatum:	2023
Sprache des Dokuments:	Englisch
Zusammenfassung/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-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-9856
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Journal of scientific computing 97
Seitenzahl oder Artikelnummer:	13
Verlag:	Springer Science + Business Media B.V.
Verlagsort:	New York, NY [u.a.]
Erscheinungsdatum:	2023
ISSN:	1573-7691
DOI der Originalveröffentlichung:	10.1007/s10915-023-02322-2
Enthalten in den Sammlungen:	DFG-491381577-H