In this paper, based on two-grid discretizations, two kinds of local and parallel finite element methods are proposed and investigated for the coupled Stokes/Darcy model. Following the idea presented in Xu and Zhou (Math. Comput. 69, 881–909 1999). a classical local and parallel finite element method is proposed and investigated. To derive global continuous approximations, a new local and parallel finite element method is devised by combining the partition of unity. We theoretically analyze the resulting formulations and derive optimal error estimates. Numerical experiments are reported to assess the theoretical results.

中文翻译：

---

Stokes / Darcy耦合模型的局部和并行有限元方法

本文在二网格离散化的基础上，提出了两种局部和并行有限元方法，用于Stokes / Darcy耦合模型。继徐周（数学COMPUT。提出的想法69，881-909 1999）。提出并研究了经典的局部并行有限元方法。为了导出全局连续逼近，通过组合单位划分，设计了一种新的局部和并行有限元方法。我们从理论上分析得出的公式并得出最佳误差估计。报道了数值实验以评估理论结果。