Solution of the radiative transfer equation in discrete ordinate form by sequential function approximation

An adaptive and scalable alternative to the finite element and finite volum e methods is developed to solve the steady multi-dimensional radiative tran sport equation. Solutions to the problem of heat transfer within a two-dime nsional box through a non-scattering medium are presented and compared to t he results from popular finite volume methods. The accuracy level of the de veloped method, using skewed piecewise linear bases, surpasses that of the finite volume results using the popular step and diamond schemes on a regul ar grid, Moreover, the accuracy levels are achieved with less than 1 % of t he number of control Volumes used by the finite volume methods. (C) 2001 Ed itions scientifiques et medicales Elsevier SAS.