approx of Young measure, Elsasser\]). We use $m=30$ “band boundaries” $\sigma_{j}$ in (\[eq:discrete approx of Young measure, Elsasser\]). \[fig:young-measure\]](young_measure_and_discrete_approx)

 

![Comparison of the exact scalar flux (\[eq:discrete scalar flux, exact\]) against its discrete approximation (\[eq:discrete scalar flux, approx\]), using $m=30$ equispaced values $\sigma_{j}$ between $1$ and $c_{\beta}$, $\beta=1$, and a single group $\left[E_{0},E_{1}\right]=\left[0,1\right]$. \[fig:transport comparison, Elsasser\]](scalar_flux_comparison_Elsasser)

A neutron transport example with absorption cross section for iron \[sub:Example-2:-iron\]
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![Watt fission spectrum](Watts_spectrum)

 

![Absorption cross section for iron.\[fig:opacity for iron\]](opacity_iron)

(a)

 

![Comparison of the exact scalar flux (\[eq:discrete scalar flux, exact\]) against its homogenized approximation (\[eq:discrete scalar flux, approx\]) and the multigroup method with Planck-weighted cross sections, using (a) $1,2024$, (b) $4,096$, (c) $16384$, and (d) $65,536$ equally spaced groups. Here the cross section is for iron as shown in Figure \[fig:opacity for iron\]. \[fig:comparison of scalar fluxes, iron\]](scalar_flux_comparison_iron_10 "fig:")        

 

(b)

  

![Comparison of the exact scalar flux (\[eq:discrete scalar flux, exact\]) against its homogenized approximation (\[eq:discrete scalar flux, approx\]) and the multigroup method with Planck-weighted cross sections, using (a) $1,2024$, (b) $4,096$, (c) $16384$, and (d) $65,536$ equally spaced groups. Here the cross section is for iron as shown in Figure \[fig:opacity for iron\]. \[fig:comparison of scalar fluxes, iron\]](scalar_flux_comparison_iron_14)

 

(c)

  

![Comparison of the 