A mixed variational framework for the radiative transfer equation

Herbert Egger*, Matthias Schlottbom

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)

Abstract

We present a rigorous variational framework for the analysis and discretization of the radiative transfer equation. Existence and uniqueness of weak solutions are established under rather general assumptions on the coefficients. Moreover, weak solutions are shown to be regular and hence also strong solutions of the radiative transfer equation. The relation of the proposed variational method to other approaches, including least-squares and even-parity formulations, is discussed. Moreover, the approximation by Galerkin methods is investigated, and simple conditions are given, under which stable quasi-optimal discretizations can be obtained. For illustration, the approximation by a finite element P N approximation is discussed in some detail.

Original languageEnglish
Article number1150014
JournalMathematical Models and Methods in Applied Sciences
Volume22
Issue number3
DOIs
Publication statusPublished - 1 Mar 2012
Externally publishedYes

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Keywords

  • Galerkin discretization
  • Mixed variational methods
  • Radiative transfer equation
  • Spherical harmonics expansion

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