In this work, a new Virtual Element Method (VEM) of arbitrary order k ≥ 2 for the time dependent Navier–Stokes equations in stream-function form is proposed and analyzed. Using suitable projection operators, the bilinear and trilinear terms are discretized by only using the proposed degrees of freedom associated with the virtual space. Under certain assumptions on the computational domain, error estimations are derived and shown that the method is optimally convergent in both space and time variables. Finally, to justify the theoretical analysis, four benchmark examples are examined numerically.
Keywords: Virtual element method, Navier–Stokes equations, time dependent problem, stream-function
@article{M2AN_2021__55_5_2535_0,
author = {Adak, Dibyendu and Mora, David and Natarajan, Sundararajan and Silgado, Alberth},
title = {A virtual element discretization for the time dependent {Navier{\textendash}Stokes} equations in stream-function formulation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2535--2566},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021058},
mrnumber = {4332962},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021058/}
}
TY - JOUR AU - Adak, Dibyendu AU - Mora, David AU - Natarajan, Sundararajan AU - Silgado, Alberth TI - A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2535 EP - 2566 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021058/ DO - 10.1051/m2an/2021058 LA - en ID - M2AN_2021__55_5_2535_0 ER -
%0 Journal Article %A Adak, Dibyendu %A Mora, David %A Natarajan, Sundararajan %A Silgado, Alberth %T A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2535-2566 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021058/ %R 10.1051/m2an/2021058 %G en %F M2AN_2021__55_5_2535_0
Adak, Dibyendu; Mora, David; Natarajan, Sundararajan; Silgado, Alberth. A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2535-2566. doi: 10.1051/m2an/2021058
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