This paper proposes a deferred defect-correction method for the time-dependent nonlinear Darcy-Brinkman model based on the mixed finite element method. The presented method combines the deferred correction strategy with the defect-correction method and involves two steps. In the first step, a defect Darcy-Brinkman model is solved. Then in the second step, a correction Darcy-Brinkman model based on the deferred correction approach is solved. Moreover, unconditional stability and convergence of the presented method are deduced. Finally, several numerical examples are given to support the theoretical analysis.

中文翻译：

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Darcy-Brinkman 模型的延迟缺陷校正有限元方法

本文提出了一种基于混合有限元方法的时变非线性Darcy-Brinkman模型延迟缺陷校正方法。所提出的方法将延迟校正策略与缺陷校正方法相结合，包括两个步骤。第一步，求解缺陷 Darcy-Brinkman 模型。然后在第二步中，求解基于延迟校正方法的校正 Darcy-Brinkman 模型。此外，还推导出了所提出方法的无条件稳定性和收敛性。最后给出了几个数值例子来支持理论分析。