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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021062
Keywords: Meshless methods, virtual element method, network element method
@article{M2AN_2021__55_5_2503_0,
author = {Coatl\'even, Julien},
title = {Basic convergence theory for the network element method},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2503--2533},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021062},
mrnumber = {4332501},
zbl = {1483.65179},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021062/}
}
TY - JOUR AU - Coatléven, Julien TI - Basic convergence theory for the network element method JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2503 EP - 2533 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021062/ DO - 10.1051/m2an/2021062 LA - en ID - M2AN_2021__55_5_2503_0 ER -
%0 Journal Article %A Coatléven, Julien %T Basic convergence theory for the network element method %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2503-2533 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021062/ %R 10.1051/m2an/2021062 %G en %F M2AN_2021__55_5_2503_0
Coatléven, Julien. Basic convergence theory for the network element method. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2503-2533. doi: 10.1051/m2an/2021062
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