• Corpus ID: 244714493

Augmented finite element formulation for the Navier--Stokes equations with vorticity and variable viscosity

@inproceedings{Anaya2021AugmentedFE,
  title={Augmented finite element formulation for the Navier--Stokes equations with vorticity and variable viscosity},
  author={Ver{\'o}nica Anaya and Ruben Caraballo and Ricardo Ruiz-Baier and H{\'e}ctor Torres},
  year={2021}
}

• Verónica Anaya, Ruben Caraballo, +1 author Héctor Torres
• Published 28 November 2021
• Mathematics

We propose and analyse an augmented mixed finite element method for the Navier–Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation includes least-squares terms arising from the constitutive equation and from the incompressibility condition, and we use a fixed point strategies to show the existence and uniqueness of continuous and discrete solutions under the assumption of sufficiently small data. The method is constructed using any compatible finite element pair for velocity and pressure as dictated by Stokes inf-sup stability, while for vorticity any generic discrete space (of arbitrary order) can be used. We establish optimal a priori error estimates. Finally, we provide a set of numerical tests in 2D and 3D illustrating the behaviour of the scheme as well as verifying the theoretical convergence rates. 2020 Mathematics Subject Classification. 65N30, 65N12, 76D07, 65N15. Updated: November 30, 2021.