THE GAUGE-UZAWA FINITE ELEMENT METHOD PART II: THE BOUSSINESQ EQUATIONS

Abstract

The Gauge-Uzawa finite element method (GU-FEM)13is a fully discrete projection type method to solve the evolution Navier–Stokes equations, which overcomes many shortcomings of projection methods and displays superior numerical performance. In this second part, we apply the GU-FEM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We show unconditional stability and error estimates for velocity, pressure and temperature, the three physical unknowns. We use a new variational approach13and realistic regularity assumptions. We conclude with two physically relevant numerical simulations, the Benard convection problem and the thermal driven cavity flow.