The stationary Darcy–Brinkman equations in the double-diffusive convection, which model the heat and mass transfer phenomena, are considered in this paper. Based on a suitable contractive operator, the existence and uniqueness of the problem are firstly proved by using the fixed point theorem. The regularities of the weak solution are also derived. Then, the Newton iterative method is studied for solving the nonlinear discrete system generated from the finite element approximation, including the stability and the optimal error estimates regarding the spatial mesh size and the iterative factor. The analysis indicates that the viscosity coefficient has more impact on the numerical algorithm than the thermal conductivity and the mass diffusivity coefficients. Finally, many numerical examples are shown to confirm the correctness of the theoretical prediction.

本文考虑了双扩散对流中的稳态Darcy-Brinkman方程，该方程模拟了传热和传质现象。首先基于不动点定理，证明了问题的存在性和唯一性。还推导了弱解的规律性。然后，研究了牛顿迭代法来求解由有限元逼近产生的非线性离散系统，包括关于空间网格大小和迭代因子的稳定性和最佳误差估计。分析表明，粘度系数对数值算法的影响大于导热系数和质量扩散系数。最后，