Simplified P-N (SPN) approximations to the equation of radiative heat transfer are applied to study the effect of internal radiation on the solid/liquid interface in Bridgman growth of semitransparent materials. An adaptive finite element method is derived for SP1 and SP2 approximations in combination with phase-change and used to simulate the solidification of a material related to BaF2. (C) 2004 Elsevier B.V. All rights reserved.