J-L Guermond and G. Kanschat,
"Asymptotic analysis of upwind dg approximation of the radiative transport equation in the diffusive limit,"
SIAM Journal of Numerical Analysis
48(1), 53-78 (2010).
We revisit some results from M. L. Adams [Nucl. Sci. Engrg., 137
(2001), pp. 298- 333]. Using functional analytic tools we prove
that a necessary and sufficient condition for the
standard upwind discontinuous
Galerkin approximation to converge to the
correct limit solution in the diffusive regime
is that the approximation space contains a linear space
of continuous functions, and the restrictions of the functions of
this space to each mesh cell contain the linear polynomials.
Furthermore, the discrete diffusion limit converges in
the Sobolev space H1 to the continuous one if the boundary
data is isotropic. With anisotropic boundary data, a boundary layer
occurs, and convergence holds in the broken Sobolev space
Hs with s < 1/2 only.
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU