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.

Beirao da Veiga, L., Dassi, F., Lovadina, C., Vacca, G. (2021). SUPG-stabilized virtual elements for diffusion-convection problems: A robustness analysis. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 55(5), 2233-2258 [10.1051/m2an/2021050].

SUPG-stabilized virtual elements for diffusion-convection problems: A robustness analysis

Beirao da Veiga, L
;
Dassi, F;Vacca, G
2021

Abstract

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.
Articolo in rivista - Articolo scientifico
Convection dominated problems; Polygonal meshes; SUPG stabilization; Virtual element method;
English
2021
55
5
2233
2258
open
Beirao da Veiga, L., Dassi, F., Lovadina, C., Vacca, G. (2021). SUPG-stabilized virtual elements for diffusion-convection problems: A robustness analysis. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 55(5), 2233-2258 [10.1051/m2an/2021050].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/341228
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