  In this paper the author reviews a version of the global Galerkin that was
developed and applied in a series of earlier publications. The method is based
on divergence-free basis functions satisfying all the linear and homogeneous
boundary conditions. The functions are defined as linear superpositions of the
Chebyshev polynomials of the first and second klinds that are combined into
divergence free vectors. The description and explanations of treatment of
boundary conditions inhomogeneities and singularities are given. Possible
implementation for steady state solvers, path-continuation, stability solvers
and straight-forward integration in time are discussed. The most important
results obtained using the approach are briefly reviewed and possible future
applications are discussed.
