Divergence free virtual elements for the stokes problem on polygonal meshes

• Published in: ESAIM. Mathematical modelling and numerical analysis Vol. 51; no. 2; pp. 509 - 535
• Main Authors: da Veiga, Lourenco Beirão, Lovadina, Carlo, Vacca, Giuseppe
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.03.2017
• Subjects: 65N12; 65N15; 65N30; 76D07; Degrees of freedom; Divergence; divergence free approximation; Error analysis; polygonal meshes; Stokes problem; Test procedures; Virtual element method
• ISSN: 0764-583X; 1290-3841
• DOI: 10.1051/m2an/2016032

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a...