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Journal of Scientific Computing

, Volume 76, Issue 2, pp 1105–1126 | Cite as

Galerkin Methods for Stationary Radiative Transfer Equations with Uncertain Coefficients

  • Xinghui ZhongEmail author
  • Qin Li
Article
  • 187 Downloads

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.

Keywords

Uncertainty quantification Radiative transfer equation Generalized polynomial chaos Convergence rate 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

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