| Issue |
ESAIM: M2AN
Volume 60, Number 1, January-February 2026
|
|
|---|---|---|
| Page(s) | 411 - 444 | |
| DOI | https://doi.org/10.1051/m2an/2026005 | |
| Published online | 11 March 2026 | |
Nitsche stabilized virtual element approximations for a Brinkman problem with mixed boundary conditions
1
GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile
2
CI 2MA, Universidad de Concepción, Concepción, Chile
3
Departamento de Ciencias, Universidad Técnica Federico Santa María, Valparaíso, Chile
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
June
2024
Accepted:
13
January
2026
Abstract
In this paper, we formulate, analyze, and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche’s technique for virtual element methods. We propose a discretization by means of the virtual elements presented in Beirão da Veiga et al. [ESAIM Math. Model. Numer. Anal. 51 (2017) 509–535]. We derive a robust stability analysis of the Nitsche stabilized discrete scheme for this model problem. We establish optimal a priori error estimates of the discrete scheme with constants independent of the viscosity. Moreover, a set of numerical tests demonstrates the robustness with respect to the physical parameters and verifies the derived convergence results.
Mathematics Subject Classification: 35Q35 / 65N15 / 65N22 / 65N30 / 76D07
Key words: Brinkman equation / slip boundary condition / virtual element methods / Nitsche method / a priori error analysis / numerical experiments
Other authors who contributed: David Mora dmora@ubiobio.c; Jesus Vellojin This email address is being protected from spambots. You need JavaScript enabled to view it.
© The authors. Published by EDP Sciences, SMAI 2026
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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