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The accuracy and stability of the least squares finite element method (LSFEM)and the Galerkin finite element method (GFEM) for solving radiative transfer inhomogeneous and inhomogeneous media are studied theoretically via a frequencydomain technique. The theoretical result confirms the traditional understandingof the superior stability of the LSFEM as compared to the GFEM. However, it isdemonstrated numerically and proved theoretically that the LSFEM will suffer adeficiency problem for solving radiative transfer in media with stronginhomogeneity. This deficiency problem of the LSFEM will cause a severeaccuracy degradation, which compromises too much of the performance of theLSFEM and makes it not a good choice to solve radiative transfer in stronglyinhomogeneous media. It is also theoretically proved that the LSFEM isequivalent to a second order form of radiative transfer equation discretized bythe central difference scheme.

A Deficiency Problem of the Least Squares Finite Element Method for Solving Radiative Transfer in Strongly Inhomogeneous Media