Volume 55, Number 5, September-October 2021
|Page(s)||2233 - 2258|
|Published online||13 October 2021|
SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis
Dipartimento di Matematica e Applicazioni, Università di Milano, Bicocca Via R. Cozzi 55, 20125 Milano, Italy
2 IMATI-CNR Pavia, Via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 20 August 2021
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al., CMAME 2016] we are able to show an “almost uniform” error bound (in the sense that the unique term that depends in an unfavourable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.
Mathematics Subject Classification: 65N15 / 65N30
Key words: Virtual element method / polygonal meshes / convection dominated problems / SUPG stabilization
© The authors. Published by EDP Sciences, SMAI 2021
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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