Title: On Fast Direct Poisson Solver, Inf-Sup Constant and Iterative
       Stokes Solver by Legendre-Galerkin Method

Author: Jie Shen

Status: J. Comput. Phys. Vol. 116, 184-188, 1995


Abstract:

We have presented in this paper a fast Poisson solver and an iterative
Stokes solver, based on the Legendre-Galerkin approximations, whose
complexities are respectively $O(N^2\log_2N)$ and $O(N^{5/2}\log_2N)$
in a two dimensional rectangular domain. Taking into account the
spectral accuracy of the Legendre-Galerkin approximations, we conclude
that these algorithms are very valuable and competitive for the
specified problems.

We have also computed numerically the
inf-sup constants of a sequence of discretized Stokes systems for a
large range of $(N,m)$. The results exhibit not only the quantitative
but also the qualitative asymptotic behavior of the inf-sup
constants. The results may serve in particular as a reference for
users of spectral methods to choose an appropriate pair of
discretization spaces for the velocity and the pressure in the Stokes
problem.