A projection-based stabilized finite element method for steady-state natural convection problem

We formulate a projection-based stabilization finite element technique for solving steady-state natural convection problems. In particular, we consider heat transport through combined solid and fluid media. This stabilization does not act on the large flow structures. Based on the projection stabilization idea, finite element error analysis of the problem is investigated and optimal errors for the velocity, temperature and pressure are established. We also present some numerical tests which both verify the theoretical predictions and demonstrate the methodʼs promise.