  We introduce a (linear) positive and asymptotic preserving method or solving
the one-group radiation transport equation. The approximation in space is
discretization agnostic: the space approximation can be done with continuous or
discontinuous finite elements (or finite volumes, or finite differences). The
method is first-order accurate in space. This type of accuracy is coherent with
Godunov's theorem since the method is linear. The two key theoretical results
of the paper are Theorem~4.4 and Theorem~4.8. The method is illustrated with
continuous finite elements. It is observed to converge with the rate $\calO(h)$
in the $L^2$-norm on manufactured solutions, and it is $\calO(h^2)$ in the
diffusion regime. Unlike other standard techniques, the proposed method does
not suffer from overshoots at the interfaces of optically thin and optically
thick regions.
