We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.
DOI : 10.1051/m2an/2015090
Keywords: Virtual element method, nonconforming method, Poisson equation, elliptic problems, unstructured meshes
Ayuso de Dios, Blanca 1, 2 ; Lipnikov, Konstantin 3 ; Manzini, Gianmarco 2, 3
@article{M2AN_2016__50_3_879_0,
author = {Ayuso de Dios, Blanca and Lipnikov, Konstantin and Manzini, Gianmarco},
title = {The nonconforming virtual element method},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {879--904},
year = {2016},
publisher = {EDP Sciences},
volume = {50},
number = {3},
doi = {10.1051/m2an/2015090},
mrnumber = {3507277},
zbl = {1343.65140},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2015090/}
}
TY - JOUR AU - Ayuso de Dios, Blanca AU - Lipnikov, Konstantin AU - Manzini, Gianmarco TI - The nonconforming virtual element method JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 879 EP - 904 VL - 50 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2015090/ DO - 10.1051/m2an/2015090 LA - en ID - M2AN_2016__50_3_879_0 ER -
%0 Journal Article %A Ayuso de Dios, Blanca %A Lipnikov, Konstantin %A Manzini, Gianmarco %T The nonconforming virtual element method %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 879-904 %V 50 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2015090/ %R 10.1051/m2an/2015090 %G en %F M2AN_2016__50_3_879_0
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