We analyze the penalty and Nitsche's methods, in the continuous and discrete senses, for the Stokes–Darcy system with a curved interface. In the continuous sense, we prove the stability and optimal convergence for the penalty approach. In discretization, the curved interface is approximated by polygonal surface. We propose the discontinuous Galerkin (DG) penalty/Nitsche schemes, and establish the stability and error analysis taking the domain perturbation into account. To obtain sharp estimates on the pressure constant and the inf-sup condition involving the integration on the interface, we study the broken $H^{1/2}$ norm of the DG element, and prove a DG version of the reversed trace operator.

我们分析了具有弯曲界面的Stokes-Darcy系统在连续和离散意义上的罚分和Nitsche方法。在连续意义上，我们证明了惩罚方法的稳定性和最优收敛性。在离散化中，弯曲的界面由多边形表面近似。我们提出了不连续的Galerkin（DG）惩罚/ Nitsche方案，并建立了考虑域扰动的稳定性和误差分析。为了获得有关界面上积分的压力常数和注入条件的精确估计，我们研究了断裂$H^{\mathrm{1个}/2}$ DG元素的范数，并证明反向跟踪算子的DG版本。