ABSTRACT: The accuracy and stabilityof the least squares finite element method (LSFEM) and the Galerkin finiteelement method (GFEM) for solving radiative transfer in homogeneous andinhomogeneous media are studied theoretically via a frequency domain technique.The theoretical result confirms the traditional understanding of the superiorstability of the LSFEM as compared to the GFEM. However, it is demonstrated numericallyand proved theoretically that the LSFEM will suffer a deficiency problem forsolving radiative transfer in media with strong inhomogeneity. Thisdeficiency problem of the LSFEM will cause a severe accuracy degradation, whichcompromises too much of the performance of the LSFEM and makes it not a goodchoice to solve radiative transfer in strongly inhomogeneous media. It is also theoreticallyproved that the LSFEM is equivalent to a second order form of radiativetransfer equation discretized by the central difference scheme.
This paper has been accepted by JQSRT. The preprint can be download here from arXiv server: http://arxiv.org/abs/1203.0615
