Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries (Advances in Applied Mathematics and Mechanics, 2011)
In this paper, we study the numerical solution of the Stokes systemin deformed axisymmetric geometries. In the azimuthal direction thediscretization is carried out by using truncated Fourier series,thus reducing the dimension of the problem. The resultingtwo-dimensional problems are discretized using the spectral elementmethod which is based on the variational formulation in primitivevariables. The meridian domain is subdivided into elements, in eachof which the solution is approximated by truncated polynomialseries. The results of numerical experiments for several geometriesare presented.