In this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of completeness, we begin recalling the corresponding well-posedness at continuous and discrete levels. After that, and with the help of a kind of a quasi-Helmholtz decomposition of functions in H(div), we develop a residual type a posteriori error analysis, deducing an estimator that is reliable and locally efficient. Finally, we provide numerical experiments, which confirm our theoretical results on the a posteriori error estimator and illustrate the performance of the corresponding adaptive algorithm, supporting its use in practice.

在这项工作中，我们将注意力集中在具有非齐次源项的斯托克斯流上，以双重混合形式表示。为了完整起见，我们开始在连续和离散级别上回顾相应的适定性。之后，在H ( d i v )中函数的一种准亥姆霍兹分解的帮助下，我们开发了一种残差类型的后验误差分析，推导出了一个可靠且局部有效的估计量。最后，我们提供了数值实验，证实了我们在后验误差估计器上的理论结果，并说明了相应自适应算法的性能，支持其在实践中的使用。