Highly efficient and local projection-based stabilized finite element method for natural convection problem

Based on two local Gauss integrations and the projection-based stabilized finite element method, a local projection-based stabilized finite element method for natural convection problem is proposed. The Oseen iteration and decoupling technique are applied to improve stability and save computational time. Compared with the common projection-based stabilized finite element method, the new method does not need to introduce any extra degree of freedom. Thus, it can save a large amount of CPU-time to get the same precision. Numerical results on the known analytical solutions, the driven cavity flow and the partitioned square enclosure problem are given to verify the theoretical predictions and demonstrate its high efficiency.