DGIMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings
In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptoticpreserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.
 Authors:

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;
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 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
 Univ. of Wisconsin, Madison, WI (United States). Department of Mathematics
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Scientific Computing
 Additional Journal Information:
 Journal Volume: 73; Journal Issue: 23; Journal ID: ISSN 08857474
 Publisher:
 Springer
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Kinetic transport equation; Uncertainty quantification; Asymptotic preserving; Random inputs; Discontinuous Galerkin; IMEX; Generalized polynomial chaos
 OSTI Identifier:
 1356966
Chen, Zheng, Liu, Liu, and Mu, Lin. DGIMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings. United States: N. p.,
Web. doi:10.1007/s1091501704392.
Chen, Zheng, Liu, Liu, & Mu, Lin. DGIMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings. United States. doi:10.1007/s1091501704392.
Chen, Zheng, Liu, Liu, and Mu, Lin. 2017.
"DGIMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings". United States.
doi:10.1007/s1091501704392. https://www.osti.gov/servlets/purl/1356966.
@article{osti_1356966,
title = {DGIMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings},
author = {Chen, Zheng and Liu, Liu and Mu, Lin},
abstractNote = {In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptoticpreserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.},
doi = {10.1007/s1091501704392},
journal = {Journal of Scientific Computing},
number = 23,
volume = 73,
place = {United States},
year = {2017},
month = {5}
}