On the stability of the Collocation method for the Radiosity equation on polyhedral domains

This paper investigates the stability of the collocation method for the radiosity equation. We introduce graded meshes and trial spaces of piecewise polynomials and prove stability for a modified collocation method. Graded meshes are necessary for higher convergence rates. The generation of triangulations which allow higher‐order approximations leads to geometrical problems which are interesting in themselves, but do not affect the stability of the collocation method.