ArXiv (open access)
Key ideas
- We consider a mixed formulations for the coupled Stokes-Darcy problem, without introducing an interface variable.
- Two finite element discretizations are considered, one based on Raviart-Thomas ($\mathbb{RT}_0$) and one based on Crouzeix-Raviart ($\mathbb{CR}_0$).
- Using weighted norms, we analyze the problem and pay special attention to the cases in which one of the subproblems has solely essential (no-flux) boundary conditions.
Main findings
- In case of essential boundary conditions in one of the subdomains, the inf-sup constant becomes parameter-dependent. However, this is due to only one parameter-dependent eigenvalue in the system.
- A norm-equivalent preconditioner is proposed and we show that the effective condition number of the preconditioned system is independent of material and discretization parameters.
