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

2012/06/20 by Lee, Young Ju, Li, Hengguang
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1206.4379

Abstract

We study the regularity and finite element approximation of the axisymmetric Stokes problem on a polygonal domain Ω. In particular, taking into account the singular coefficients in the equation and non-smoothness of the domain, we establish the well-posedness and full regularity of the solution in new weighted Sobolev spaces \maK^m_{μ, 1}(Ω). Using our a priori results, we give a specific construction of graded meshes on which the Taylor-Hood mixed method approximates singular solutions at the optimal convergence rate. Numerical tests are presented to confirm the theoretical results in the paper.

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