Towards Stable Radial Basis Function Methods for Linear Advection Problems
| Autor: | Philipp Öffner, Élise Le Mélédo, Jan Glaubitz |
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| Přispěvatelé: | University of Zurich, Glaubitz, Jan |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Work (thermodynamics)
Advection Scalar (physics) Numerical Analysis (math.NA) 35L65 41A05 41A30 65D05 65M12 Stability (probability) Computational Mathematics 10123 Institute of Mathematics 510 Mathematics Computational Theory and Mathematics Modeling and Simulation Path (graph theory) FOS: Mathematics Applied mathematics Radial basis function Boundary value problem Mathematics - Numerical Analysis 2605 Computational Mathematics Energy (signal processing) Mathematics 2611 Modeling and Simulation 1703 Computational Theory and Mathematics |
| Popis: | 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. To appear in Computers and Mathematics with Applications |
| Databáze: | OpenAIRE |
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