| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1365 - 1397 | |
| DOI | https://doi.org/10.1051/m2an/2025023 | |
| Published online | 27 May 2025 | |
A nonconforming virtual element method for advection–diffusion–reaction problems with CIP stabilization
1
Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy
2
IMATI-CNR, Via Adolfo Ferrata 5, 27100 Pavia, Italy
3
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
4
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via Roberto Cozzi 55, 20125 Milano, Italy
* Corresponding author: manuel.trezzi@unimib.it
Received:
16
July
2024
Accepted:
25
March
2025
We study a nonconforming virtual element method (VEM) for advection–diffusion–reaction problems with continuous interior penalty (CIP) stabilization. The design of the method is based on a standard variational formulation of the problem (no skew-symmetrization), and boundary conditions are imposed with a Nitsche technique. We use the enhanced version of VEM, with a “dofi-dofi” stabilization in the diffusion and reaction terms. We prove stability of the proposed method and derive h-version error estimates.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15
Key words: Virtual element method / continuous interior penalty / advection–diffusion–reaction
© The authors. Published by EDP Sciences, SMAI 2025
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