Radiative transfer with finite differences and finite elements

Finite Difference and Finite Element algorithms for the solution of the radiative transfer equation as required for the modeling of modern high quality observations are briefly described and discussed. It is emphasized that in the Finite Element approach there is the possibility to obtain an a-posteriori error estimator, which allows to locally refine the grid and in this way to obtain numerical solutions that do not differ from the (unknown) analytical solutions by more than a prescribed tolerance.