Abstract
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.
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Acknowledgements
X. Zhong is supported by the start-up funds from Zhejiang University and funds from Recruitment Program for Young Professionals (No. 588020-X01702/105). X. Zhong is also supported in part by the Funds for Creative Research Groups of NSFC (No. 11621101). Q. Li is supported by the start-up funds from UW-Madison and NSF 1619778.
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Zhong, X., Li, Q. Galerkin Methods for Stationary Radiative Transfer Equations with Uncertain Coefficients. J Sci Comput 76, 1105–1126 (2018). https://doi.org/10.1007/s10915-018-0652-7
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DOI: https://doi.org/10.1007/s10915-018-0652-7