Approximation of Axisymmetric Darcy Flow
نویسنده
چکیده
In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data. 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 the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) approximation pairs are shown to be LBB stable, and corresponding a priori error estimates derived. Presented numerical experiments confirm the predicted rates of convergence for the RT and BDM approximations.
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