Convergence of several iterations for double‐diffusive natural convection model

Abstract

Several iterative finite element methods are analyzed for a steady‐state double‐diffusive natural convection model, which contains the diffusion of temperature and concentration and can simulate heat and mass transfer phenomena. These iterations include the Stokes‐type, Newton‐type, and Oseen‐type iterative methods. Then, based on the uniqueness condition, stability and convergence of these iterative methods are proved for the considered model. Finally, some numerical examples are presented for validating the correctness of the theoretical analysis.