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Towards stable radial basis function methods for linear advection problems


Glaubitz, Jan; Le Mélédo, Elise; Öffner, Philipp (2021). Towards stable radial basis function methods for linear advection problems. Computers & Mathematics with Applications, 85:84-97.

Abstract

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoretical analysis

Abstract

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoretical analysis

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Modeling and Simulation
Physical Sciences > Computational Theory and Mathematics
Physical Sciences > Computational Mathematics
Language:English
Date:1 March 2021
Deposited On:03 Nov 2021 13:57
Last Modified:27 Mar 2024 02:50
Publisher:Elsevier
ISSN:0898-1221
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.camwa.2021.01.012
Project Information:
  • : FunderDeutsche Forschungsgemeinschaf
  • : Grant IDGL 927/1-1
  • : Project Title
  • : FunderSNSF
  • : Grant ID200020_175784
  • : Project TitleSolving advection dominated problems with high order schemes with polygonal meshes: application to compressible and incompressible flow problems
  • : FunderUZH Postdoc Forschungskredit
  • : Grant IDFK-19-104
  • : Project Title
  • Content: Accepted Version
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)