# 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} }

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…

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