A Uzawa-Type Iterative Algorithm for the Stationary Natural Convection Model.

In this study, a Uzawa-type iterative algorithm is introduced and analyzed for solving the stationary natural convection model, where physical variables are discretized by utilizing a mixed finite element method. Compared with the common Uzawa iterative algorithm, the main finding is that the proposed algorithm produces weakly divergence-free velocity approximation. In addition, the convergence results of the proposed algorithm are provided, and numerical tests supporting the theory are presented.

Finite Element Iterative Methods for the Stationary Double-Diffusive Natural Convection Model.

In this paper, we consider the stationary double-diffusive natural convection model, which can model heat and mass transfer phenomena. Based on the fixed point theorem, the existence and uniqueness of the considered model are proved. Moreover, we design three finite element iterative methods for the considered problem.