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Journal of Scientific Computing

, Volume 78, Issue 2, pp 864–886 | Cite as

A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes

  • Long Chen
  • Feng WangEmail author
Article

Abstract

Some virtual element methods on polytopal meshes for the Stokes problem are proposed and analyzed. The pressure is approximated by discontinuous polynomials, while the velocity is discretized by H(div) virtual elements enriched with some tangential polynomials on the element boundaries. A weak symmetric gradient of the velocity is computed using the corresponding degree of freedoms. The main feature of the method is that it exactly preserves the divergence free constraint, and therefore the error estimates for the velocity does not explicitly depend on the pressure.

Keywords

Stokes equations Virtual element methods H(div) element Divergence free 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingChina
  2. 2.Department of MathematicsUniversity of California at IrvineIrvineUSA
  3. 3.Jiangsu Key Laboratory for NSLSCS, School of Mathematical SciencesNanjing Normal UniversityNanjingChina

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