We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We
reduce the original problem by a Fourier expansion in the angular variable to a countable
family of two-dimensional problems. We decompose the meridian domain, assumed polygonal,
in a finite number of rectangles and we discretize by a spectral method. Then we describe
the main features of the mortar method and use the algorithm Strang Fix to improve the
accuracy of our discretization.