| Issue |
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
|
|
|---|---|---|
| Page(s) | 3303 - 3334 | |
| DOI | https://doi.org/10.1051/m2an/2023075 | |
| Published online | 29 November 2023 | |
The nonconforming virtual element method for Oseen’s equation using a stream-function formulation
1
GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile
2
IMATI, Consiglio Nazionale delle Ricerche, via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: dibyendu.jumath@gmail.com
Received:
30
August
2022
Accepted:
4
September
2023
We approximate the solution of the stream function formulation of the Oseen equations on general domains by designing a nonconforming Morley-type virtual element method. Under a suitable assumption on the continuous problem’s coefficients, the discrete scheme is well-posed. By introducing an enriching operator, we derive an a priori estimate of the error in a discrete H2 norm. By post-processing the discrete stream function, we compute the discrete velocity and vorticity fields. Furthermore, we recover an approximate pressure field by solving a Stokes-like problem in a nonconforming Crouzeix–Raviart-type virtual element space that is in a Stokes-complex relation with the Morley-type space of the virtual element approximation. Finally, we confirm our theoretical estimates by solving benchmark problems that include a convex and a nonconvex domain.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15 / 35K25
Key words: Oseen’s equation / nonconforming VEM / a priori estimate / enriching operator / Morley element
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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