In this paper we introduce two full multigrid algorithms in a Cartesian and a Polar coordinate system that have
been modified to treat the elliptic partial differential equations with a mixed derivative term, in the two dimensional space
in a quarter of a unit circle, special modification for the points in the neighborhood of the curved boundary has been done.
An advantage of the two algorithms is that the extension from two to three space dimensions is straightforward. numerical
examples have been given.