Published version ArXiv (open access)
Summary
- We discretize the Stokes equations with the Marker-and-Cell (MAC) method and Darcy flow using the Raviart-Thomas pair.
- We analyze the MAC scheme by interpreting it as a conforming mixed finite element method on a staggered grid.
- The two schemes are coupled by introducing a Lagrange multiplier on the Stokes-Darcy interface that enforces flux continuity.
- We show that the discrete system is well-posed and provide a priori error estimates.
- The analytical results are validated by three numerical test cases.