Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry

@article{Graham2019ErrorAA,
  title={Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry},
  author={Ivan G. Graham and M Parkinson and Robert Scheichl},
  journal={IMA Journal of Numerical Analysis},
  year={2019}
}
We present an analysis of multilevel Monte Carlo (MLMC) techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients (cross-sections) are heterogenous random fields. To do this we first give a new error analysis for the combined spatial and angular discretisation in the deterministic case, with error estimates that are explicit in the coefficients (and allow for very low regularity and jumps). This detailed error analysis is done… 
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