Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations.

*(English)* Zbl 1254.76051
Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer (ISBN 88-470-0180-3/hbk). 3-20 (2003).

Summary: We introduce a differential system based on the coupling of the (Navier) Stokes equations and the Darcy equation for the modelling of the interaction between surface and subsurface flows. We formulate the problem as an interface problem and analyze the associated Steklov-PoincarĂ© operator. We then propose a way of solving the coupled problem iteratively, based on a suitable splitting of the interface conditions, allowing the solution of two subproblems at each step.

##### MSC:

76D05 | Navier-Stokes equations (fluid dynamics) |

76M25 | Other numerical methods (fluid mechanics) |