| Issue |
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
|
|
|---|---|---|
| Page(s) | 2535 - 2566 | |
| DOI | https://doi.org/10.1051/m2an/2021058 | |
| Published online | 01 November 2021 | |
A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
1
GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile
2
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
3
CI 2MA, Universidad de Concepción, Concepción, Chile
* Corresponding author: dadak@ubiobio.cl, dibyendu.jumath@gmail.com
Received:
4
April
2021
Accepted:
15
September
2021
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.
Mathematics Subject Classification: 65N30 / 65N12 / 76D07 / 65N15
Key words: Virtual element method / Navier–Stokes equations / time dependent problem / stream-function
© The authors. Published by EDP Sciences, SMAI 2021
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