Stationary radiative transfer with vanishing absorption

Herbert Egger*, Matthias Schlottbom

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

We investigate the unique solvability of radiative transfer problems without strictly positive lower bounds on the absorption and scattering parameters. The analysis is based on a reformulation of the transfer equation as a mixed variational problem with penalty term for which we establish the well-posedness. We also prove stability of the solution with respect to perturbations in the parameters. This allows to approximate stationary radiative transfer problems by even-parity formulations even in the case of vanishing absorption. The mixed variational framework used for the analysis also enables a systematic investigation of discretization obtained by Galerkin methods. We show that, in contrast to the full problem, the widely used P N-approximations, and discretizations based on these, are not stable in the case of vanishing absorption. Some consequences and possible remedies yielding stable approximations are discussed.

Original languageEnglish
Pages (from-to)973-990
Number of pages18
JournalMathematical Models and Methods in Applied Sciences
Volume24
Issue number5
DOIs
Publication statusPublished - 1 May 2014
Externally publishedYes

Keywords

  • Even-parity formulation
  • Mixed variational problems
  • Stationary radiative transfer
  • Vanishing absorption

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