Radiative transfer with finite elements - I. Basic method and tests

A finite element method for solving the monochromatic radiation transfer eq uation including scattering in three dimensions is presented. The algorithm employs unstructured grids which are adaptively refined. Adaptivity as wel l as ordinate parallelization reduce memory requirements and execution time and make it possible to calculate the radiation field across several lengt h scales for objects with strong opacity gradients. An a posteriori error e stimate for one particular quantity is obtained by solving the dual problem . The application to a sample of test problems reveals the properties of th e implementation.