Virtual Element Method for the Navier--Stokes Equation coupled with the Heat Equation

  • Antonietti, Paola Francesca (Politecnico di Milano)
  • Vacca, Giuseppe (University of Bari)
  • Verani, Marco (Politecnico di Milano)

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We consider the Virtual Element discretization of the Navier-Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We introduce the Virtual Element discretization of the coupled problem, show its well-posedness, and prove optimal error estimates. Finally, numerical experiments confirming the theoretical error bounds are also presented.