113 research outputs found
A Deficiency Problem of the Least Squares Finite Element Method for Solving Radiative Transfer in Strongly Inhomogeneous Media
The accuracy and stability of the least squares finite element method (LSFEM)
and the Galerkin finite element method (GFEM) for solving radiative transfer in
homogeneous and inhomogeneous media are studied theoretically via a frequency
domain technique. The theoretical result confirms the traditional understanding
of the superior stability of the LSFEM as compared to the GFEM. However, it is
demonstrated numerically and proved theoretically that the LSFEM will suffer a
deficiency problem for solving radiative transfer in media with strong
inhomogeneity. This deficiency problem of the LSFEM will cause a severe
accuracy degradation, which compromises too much of the performance of the
LSFEM and makes it not a good choice to solve radiative transfer in strongly
inhomogeneous media. It is also theoretically proved that the LSFEM is
equivalent to a second order form of radiative transfer equation discretized by
the central difference scheme
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