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

Authors:
Young-Ju Lee;Hengguang Li
Affiliations:
Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, United States;Department of Mathematics, Wayne State University, Detroit, MI 48202, United States
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

We study the regularity and finite element approximation of the axisymmetric Stokes problem on a polygonal domain @W. 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 K"@m","1^m(@W). 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.