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.
Keywords: Virtual element method, polygonal meshes, convection dominated problems, SUPG stabilization
@article{M2AN_2021__55_5_2233_0,
author = {Beir\~ao da Veiga, Lourenco and Dassi, Franco and Lovadina, Carlo and Vacca, Giuseppe},
title = {SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2233--2258},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021050},
mrnumber = {4323403},
zbl = {1490.65267},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021050/}
}
TY - JOUR AU - Beirão da Veiga, Lourenco AU - Dassi, Franco AU - Lovadina, Carlo AU - Vacca, Giuseppe TI - SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2233 EP - 2258 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021050/ DO - 10.1051/m2an/2021050 LA - en ID - M2AN_2021__55_5_2233_0 ER -
%0 Journal Article %A Beirão da Veiga, Lourenco %A Dassi, Franco %A Lovadina, Carlo %A Vacca, Giuseppe %T SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2233-2258 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021050/ %R 10.1051/m2an/2021050 %G en %F M2AN_2021__55_5_2233_0
Beirão da Veiga, Lourenco; Dassi, Franco; Lovadina, Carlo; Vacca, Giuseppe. SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2233-2258. doi: 10.1051/m2an/2021050
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