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 H1/2 norm of the DG element, and prove a DG version of the reversed trace operator.
- Discontinuous Galerkin method
- Nitsche's method
- Penalty method
- Stokes–Darcy system