SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis
Numerical Analysis
2020-12-03 v1 Numerical Analysis
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 unfavorable 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.
Cite
@article{arxiv.2012.01104,
title = {SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis},
author = {L. Beirão da Veiga and F. Dassi and C. Lovadina and G. Vacca},
journal= {arXiv preprint arXiv:2012.01104},
year = {2020}
}