Variational multiscale virtual element method for the convection-dominated diffusion problem
type: Item
instance of: scholarly article
title: Variational multiscale virtual element method for the convection-dominated diffusion problem
zbMATH Open document ID: 1468.65207
author: Cong Xie
author: Gang Wang
author: Xinlong Feng
published in: Applied Mathematics Letters
publication date: 2021-04-28T00:00:00Z
review text: The authors propose and analyze a stabilized multiscale virtual element method for the numerical solution of convection-diffusion equations on two-dimensional polygonal domains, which are equipped with homogeneous Dirichlet boundary conditions. The focus is on the equations with the dominated convection term, which makes the numerical solution a challenging problem because without any stabilization spurious oscillations can occur. The proposed method combines a variational multiscale method and a virtual element method with linear elements. The stabilization term is symmetric, positive, and does not depend on any parameter that has to be chosen by the user. Furthermore, compared to other stabilization techniques for these types of equations, the advantage is also the simple computation of the stabilization term. The authors analyze the stability of the proposed method and derive error estimates with respect to the \(L^2\) and \(H^1\) norms. Numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the proposed method.
reviewed by: Dana Černá
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7340763
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: dominated convection
zbMATH Keywords: virtual element method
zbMATH Keywords: stabilized method
zbMATH Keywords: variational multiscale method
MaRDI profile type: Publication
full work available at URL: j.aml.2021.107077
OpenAlex ID: W3130794243
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DOI: 10.1016/J.AML.2021.107077
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description: scientific article; zbMATH DE number 7340763