Name: Vincent J. Ervin Title: Approximation of Darcy Fluid Flow equations in an Axisymmetric Domain Abstract: Motivated by the approximation of fluid flow in the eye (modeled by coupled Stokes-Darcy fluid flow equations) we consider the approximation of Darcy fluid flow equations in an axisymmetric domain. 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. (Notable is that in this setting, for (Xh, Qh) denoting the velocity and pressure approximation spaces for Raviart-Thomas approximating elements, divergence(Xh) is not equal to Qh.) We will show that in this setting the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) approximation pairs are LBB stable, and present corresponding a priori error estimates. Numerical experiments supporting the predicted rates of convergence for the RT and BDM approximations will also be given.