Energy-stable global radial basis function methods on summation-by-parts form

Thumbnail Image

Files

energystable_global_radial_ba-20240119122453686.pdf (1.12 MB)

Date issued

2024

Authors

Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Reuse License

CC-BY-4.0
Description of rights: CC-BY-4.0
Item type: Item , ZeitschriftenaufsatzAccess status: Open Access ,

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.

DOI

http://doi.org/10.25358/openscience-9960

Description

Keywords

Citation

URI

https://openscience.ub.uni-mainz.de/handle/20.500.12030/9978

Published in

Journal of scientific computing, 98, Springer Science + Business Media B.V., New York, NY u.a., 2024, https://doi.org/10.1007/s10915-023-02427-8

Relationships

Collections

DFG-491381577-H

Endorsement

Review

Supplemented By

Referenced By