| Issue |
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
|
|
|---|---|---|
| Page(s) | 2503 - 2533 | |
| DOI | https://doi.org/10.1051/m2an/2021062 | |
| Published online | 29 October 2021 | |
Basic convergence theory for the network element method
IFP Énergies nouvelles, 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France
* Corresponding author: julien.coatleven@ifpen.fr
Received:
24
February
2021
Accepted:
26
September
2021
A recent paper introduced the network element method (NEM) where the usual mesh was replaced by a discretization network. Using the associated network geometric coefficients and following the virtual element framework, a consistent and stable numerical scheme was proposed. The aim of the present paper is to derive a convergence theory for the NEM under mild assumptions on the exact problem. We also derive basic error estimates, which are sub-optimal in the sense that we have to assume more regularity than usual.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15
Key words: Meshless methods / virtual element method / network element method
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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