Abstract
In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data, using mixed finite element methods. Rewriting the problem in cylindrical coordinates reduces the three-dimensional problem to a problem in two dimensions. This reduction to two dimensions requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting the Raviart--Thomas (RT) and Brezzi--Douglas--Marini (BDM) approximation pairs are shown to be LBB stable and corresponding a priori error estimates are derived. Presented numerical experiments confirm the predicted rates of convergence for the RT and BDM approximations.
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