| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 2007 - 2040 | |
| DOI | https://doi.org/10.1051/m2an/2023040 | |
| Published online | 03 July 2023 | |
A conservative network element method for diffusion-advection-reaction problems
IFP Énergies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
* Corresponding author: julien.coatleven@ifpen.fr
Received:
13
January
2023
Accepted:
28
April
2023
We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15
Key words: Meshless methods / variational method / network element method
© The authors. Published by EDP Sciences, SMAI 2023
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