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.
SUPG-stabilized virtual elements for diffusion-convection problems: A robustness analysis / L.B. Da Veiga, F. Dassi, C. Lovadina, G. Vacca. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 55:5(2021), pp. 2233-2258. [10.1051/m2an/2021050]
SUPG-stabilized virtual elements for diffusion-convection problems: A robustness analysis
C. LovadinaPenultimo
;
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.File | Dimensione | Formato | |
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