Radiative transfer in moving media I. Discontinuous finite element method for one-dimensional atmospheres

We describe the solution of the one-dimensional radiative transfer equation using the discontinuous finite element method. Tests of this method prove its reliability for static media. The static solution is then applied to the solution of the transfer equation in a moving medium using a method which we call here the Local Lorentz Transformation (LLT) method. This new method is applicable also to non-monotonic velocity fields. Direct solution of the radiative transfer equation in the moving medium using the discontinuous finite element method is also presented for cases both with and without inclusion of the effect of aberration. All three techniques are compared and they give comparable results.