In this paper, a global Galerkin method is used numerically to solve the exterior Dirichlet problem for the Radiosity equation for the sphere, perturbation of the sphere, ellipsoid and the oval of Cassini in three dimensions. The Radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces when their reflectivity and emissivity are given. Theoretical and computational details of the method for small reflectivity values are presented.

Dirichlet problem, Radiosity equation, Galerkin method.