An Adaptive Higher Order Method for Solving the Radiation Transport Equation on Unstructured Grids

A new class of solution methods based on a short-characteristics approach embedded in the finite element framework for the solution of the radiation transport equation is developed and tested. The order of convergence and the error to runtime ratio are determined in numerical tests. Furthermore, the efficiency of the scheme is demonstrated in the case of a challenging problem from the field of solar physics. A quantitative comparison with other methods, based either on the characteristics or on the finite element approach, is carried out. This emphasizes the efficiency and accuracy of our method. Two different adaptation mechanisms are studied: grid adaptation and local variation of the order of the scheme.