Approximation of coupled Stokes–Darcy flow in an axisymmetric domain

In this article we investigate the numerical approximation of coupled Stokes and Darcy fluid flow equations in an axisymmetric domain. The fluid flow is assumed to be axisymmetric. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting we show that the proposed approximation scheme has a unique solution, and derive corresponding a priori error estimate. Computations for an example with a know solution are presented which support the a priori error estimate. Computations are also given for a model of fluid flow in the eye.