Autoren:	Glaubitz, Jan Nordström, Jan Öffner, Philipp
Titel:	Energy-stable global radial basis function methods on summation-by-parts form
Online-Publikationsdatum:	25-Jan-2024
Erscheinungsdatum:	2024
Sprache des Dokuments:	Englisch
Zusammenfassung/Abstract:	Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial differential equations, only a few stability results are known. In particular, if boundary conditions are included, stability issues frequently occur. The question we address in this paper is how provable stability for RBF methods can be obtained. We develop a stability theory for global radial basis function methods using the general framework of summation-by-parts operators often used in the Finite Difference and Finite Element communities. Although we address their practical construction, we restrict the discussion to basic numerical simulations and focus on providing a proof of concept.
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-9960
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Journal of scientific computing 98
Seitenzahl oder Artikelnummer:	30
Verlag:	Springer Science + Business Media B.V.
Verlagsort:	New York, NY u.a.
Erscheinungsdatum:	2024
ISSN:	1573-7691
DOI der Originalveröffentlichung:	10.1007/s10915-023-02427-8
Enthalten in den Sammlungen:	DFG-491381577-H