Spectral element methods for axisymmetric Stokes problems

The approximation of the Stokes problem in axisymmetric geometries using th e spectral element method is considered. The presence of the volume element r dr dz in the weak formulation of the problem is shown to be a potential source of difficulty. The discrete equations associated with nodes on the a xis of symmetry can lead to a degeneracy in the global system of equations. This difficulty is resolved by incorporating the factor r into the weight function for spectral elements adjacent to the axis of symmetry and using a ppropriate basis functions in these elements in the radial direction. Prope rties of the Jacobi polynomials are used to construct the elements of the m odified method. Numerical results are presented demonstrating some of the f eatures of the proposed approach. (C) 2000 Academic Press.