In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of the von Kármán equations, which describe the deformation of very thin elastic plates. We consider a variational formulation in terms of two variables: the transverse displacement of the plate and the Airy stress function. The VEM scheme is conforming in H2 for both variables and has the advantages of supporting general polygonal meshes and is simple in terms of coding aspects. We prove that the discrete problem is well posed for h small enough and optimal error estimates are obtained. Finally, numerical experiments are reported illustrating the behavior of the virtual scheme on different families of meshes.
Keywords: Virtual element method, von Kármán equations, error estimates, polygonal meshes
@article{M2AN_2021__55_2_533_0,
author = {Lovadina, Carlo and Mora, David and Vel\'asquez, Iv\'an},
title = {A virtual element method for the von {K\'arm\'an} equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {533--560},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {2},
doi = {10.1051/m2an/2020085},
mrnumber = {4229191},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020085/}
}
TY - JOUR AU - Lovadina, Carlo AU - Mora, David AU - Velásquez, Iván TI - A virtual element method for the von Kármán equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 533 EP - 560 VL - 55 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020085/ DO - 10.1051/m2an/2020085 LA - en ID - M2AN_2021__55_2_533_0 ER -
%0 Journal Article %A Lovadina, Carlo %A Mora, David %A Velásquez, Iván %T A virtual element method for the von Kármán equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 533-560 %V 55 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020085/ %R 10.1051/m2an/2020085 %G en %F M2AN_2021__55_2_533_0
Lovadina, Carlo; Mora, David; Velásquez, Iván. A virtual element method for the von Kármán equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 2, pp. 533-560. doi: 10.1051/m2an/2020085
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