Divergence free Virtual Elements for the Stokes problem on polygonal meshes

Abstract

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 relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with less degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.

Cited by in corpus (4)

• A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations
• A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems
• Exponential convergence of the hp Virtual Element Method with corner singularities
• Mimetic Spectral Element Method for Anisotropic Diffusion