Abstract In this article, a grad-div stabilized projection finite element method is proposed for the double-diffusive natural convection model. Moreover, for the presented method, the stability analysis, and error estimates are deduced. Finally, numerical tests are provided that demonstrate the efficiency of the method. It is found that the presented method can improve the accuracy of the solution compared with the standard projection method, and compute approximations with better mass conservation.

中文翻译：

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双扩散自然对流模型的梯度-div稳定投影有限元方法

摘要 本文针对双扩散自然对流模型提出了梯度-div稳定投影有限元方法。此外，对于所提出的方法，稳定性分析和误差估计被推导出来。最后，提供了数值测试，证明了该方法的有效性。结果表明，与标准投影方法相比，所提出的方法可以提高解的精度，并计算出具有更好质量守恒的近似值。