Asymptotic analysis of a computational method for time- and frequency-dependent radiative transfer (Q1275179)

An asymptotic analysis of a time-dependent, energy-dependent, nonlinear radiative transfer problem in which opacities are large \((O(\varepsilon^{-1}))\) and interior sources are small \((O(\varepsilon))\) usually leads, as \(\varepsilon\to 0\), to the equilibrium diffusion equation in the interior of the system, along with boundary conditions and initial conditions. The authors apply the same asymptotic analysis to a discrete version of the problem. They show, as \(\varepsilon\to 0\), that the discrete solution satisfies a robust discretized version of the correct equilibrium diffusion equation with highly accurate boundary and initial conditions. They consider numerical results which verify their predictions.