In this paper, based on two-grid discretization, a new local and parallel finite element method is proposed and investigated for the mixed Navier–Stokes–Darcy problem. Compared with the classical local and parallel finite element method, the main features of our method are: (1) partition of unity method is considered to generate local subproblems; (2) global continuous approximations are achieved. We theoretically analyze the proposed method and report on some numerical tests to support the theoretical results.

中文翻译：

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Navier–Stokes–Darcy混合问题的一种新颖的局部和并行有限元方法

本文基于两网格离散化，提出了一种新的局部和并行有限元方法，并研究了混合的Navier–Stokes–Darcy问题。与经典的局部和并行有限元方法相比，我们的方法的主要特点是：（1）统一方法的划分被认为产生局部子问题；（2）实现了全局连续逼近。我们从理论上分析了所提出的方法，并报告了一些数值测试以支持理论结果。