| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2809 - 2836 | |
| DOI | https://doi.org/10.1051/m2an/2025076 | |
| Published online | 15 October 2025 | |
A pressure-robust virtual element method for the Stokes problem
Department of Mathematics, Shandong University, Jinan 250100, P.R. China
* Corresponding author: hxrui@sdu.edu.cn
Received:
25
February
2025
Accepted:
7
September
2025
We present an arbitrary-order pressure-robust nonconforming virtual element method for the Stokes problem. Based on the local subtriangulations of polygons and the requirement of recovering the orthogonality between the velocity virtual space and the gradient forces, we introduce a computable reconstruction operator by modifying the classical Brezzi–Douglas–Marini interpolation operator. Under the shape regularity conditions, we show that the broken H1-semi-norm and L2-norm estimates of the velocity are independent of the pressure and the viscosity coefficient, and achieve the optimal convergence rates. Numerical results confirm the pressure-robust property and the uniform convergence of the method, especially when higher-order approximations are used.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 76M10
Key words: Nonconforming virtual element / Stokes problem / pressure-robustness / divergence-preserving reconstruction / general meshes
© The authors. Published by EDP Sciences, SMAI 2025
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