A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed finite element pair in the Darcy domain. Due to this choice, the method conserves linear momentum and mass locally in the Stokes domain and exhibits local mass conservation in the Darcy domain. The MAC scheme is reformulated as a mixed finite element method on a staggered grid, which allows for the proposed scheme to be analyzed as a mortar mixed finite element method. We show that the discrete system is well-posed and derive a priori error estimates that indicate first order convergence in all variables. The system can be reduced to an interface problem concerning only the mortar variables, leading to a non-overlapping domain decomposition method. Numerical examples are presented to illustrate the theoretical results and the applicability of the method.

翻译：针对耦合Stokes-Darcy问题，本文提出一种非匹配网格离散方法，该方法利用界面上的砂浆变量，将Stokes域中的标记点与网格（MAC）方法与Darcy域中的Raviart-Thomas混合有限元对进行耦合。由于这一选择，该方法在Stokes域局部守恒线性动量与质量，并在Darcy域实现局部质量守恒。MAC格式被重构为交错网格上的混合有限元方法，从而可将所提方案作为砂浆混合有限元方法进行分析。我们证明离散系统是适定的，并推导出先验误差估计，表明所有变量均具有一阶收敛性。该系统可简化为仅涉及砂浆变量的界面问题，从而得到一种非重叠区域分解方法。数值算例验证了理论结果及该方法的适用性。