| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
|---|---|---|
| Page(s) | S301 - S321 | |
| DOI | https://doi.org/10.1051/m2an/2020032 | |
| Published online | 26 February 2021 | |
On particles and splines in bounded domains
Center for Computational Engineering Science, Mathematics Division, RWTH Aachen University, Aachen, Germany
* Corresponding author: kirchhart@mathcces.rwth-aachen.de
Received:
18
February
2019
Accepted:
28
April
2020
We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain’s boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in Ws,p-norms, s ∈ ℝ, 1 ≤ p ≤ ∞.
Mathematics Subject Classification: 65M75 / 65M85 / 65D07 / 65D32
Key words: Particle methods / splines / fictitious domains / ghost penalty
© EDP Sciences, SMAI 2021
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