Authors:	Glaubitz, Jan Nordström, Jan Öffner, Philipp
Title:	Energy-stable global radial basis function methods on summation-by-parts form
Online publication date:	25-Jan-2024
Year of first publication:	2024
Language:	english
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:	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-9960
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 98
Pages or article number:	30
Publisher:	Springer Science + Business Media B.V.
Publisher place:	New York, NY u.a.
Issue date:	2024
ISSN:	1573-7691
Publisher DOI:	10.1007/s10915-023-02427-8
Appears in collections:	DFG-491381577-H