The simulation of astrophysical radiative transfer problems (RTP) is a hard task. On the one hand, the high dimension of the computational domain (3 space, 2 ordinate and 1 frequency variables) calls for huge amounts of memory even for coarse discretisations. On the other hand, accretion discs show very localised features, making a high resolution in some regions of the disk necessary. Furthermore, there should be an estimate of the numerical errors to avoid physical misinterpretation.

Apart from the usage of parallel machines with their big memory to enable the computation of RTP’s, we developed a means to generate nearly optimal discretisation meshes. Combined with efficient error estimates, we can solve RTP’s to a very high guaranteed accuracy. These estimates, weighted residual a posteriori error estimates, can not only control global error quantities like the mean quadratic error or the error in the energy norm. They can be suited to nearly any error functional.