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We study the regularity and finite element approximation of the axisymmetricStokes problem on a polygonal domain $\Omega$. In particular, taking intoaccount the singular coefficients in the equation and non-smoothness of thedomain, we establish the well-posedness and full regularity of the solution innew weighted Sobolev spaces $\maK^m_{\mu, 1}(\Omega)$. Using our a prioriresults, we give a specific construction of graded meshes on which theTaylor-Hood mixed method approximates singular solutions at the optimalconvergence rate. Numerical tests are presented to confirm the theoreticalresults in the paper.

Axisymmetric Stokes equations in polygonal domains: regularity and finite element approximations