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.
|Number of pages||18|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 1 May 2014|
- Even-parity formulation
- Mixed variational problems
- Stationary radiative transfer
- Vanishing absorption