Galerkin Methods for Stationary Radiative Transfer Equations with Uncertain Coefficients

In this paper we study the stationary radiative transfer equation with random coefficients. Galerkin methods are applied, which use orthogonal polynomials associated with the probability distribution of the random variables as basis functions in the random space. Such algorithms have been widely used for kinetic equations with random inputs, however, the corresponding numerical analysis is rare. In this paper we establish regularity theorems describing the smoothness properties of the solution, and investigate the convergence rate of N-term truncated polynomials under the spectral method framework. Numerical tests are conducted to demonstrate our analytical results.