  A general local Fourier analysis for overlapping block smoothers on
triangular grids is presented. This analysis is explained in a general form for
its application to problems with different discretizations. This tool is
demonstrated for two different problems: a stabilized linear finite element
discretization of Stokes equations and an edge-based discretization of the
curl-curl operator by lowest-order N\'ed\'elec finite element method. In this
latter, special Fourier modes have to be considered in order to perform the
analysis. Numerical results comparing two- and three-grid convergence factors
predicted by the local Fourier analysis to real asymptotic convergence factors
are presented to confirm the predictions of the analysis and show their
usefulness.
