Uniform spectral convergence of the

Shi Jin University of Wisconsin-Madison Jian-Guo Liu Duke University Zheng Ma Shanghai Jiao Tong Unviersity

Numerical Analysis and Scientific Computing mathscidoc:1702.25019

2017.1
In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scal- ing. We first establish uniform (in the Knudsen number) stability results in the random space for the transport equation with uncertain scattering coefficients, and then prove the uniform spectral conver- gence (and consequently the sharp stochastic Asymptotic-Preserving property) of the stochastic Galerkin method. A micro-macro decom- position based fully discrete scheme is adopted for the problem and proved to have a uniform stability. Numerical experiments are conducted to demonstrate the stability and asymptotic properties of the method.
linear transport equation, random inputs, diffusion limit, uncertainty quanti
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@inproceedings{shi2017uniform,
  title={Uniform spectral convergence of the},
  author={Shi Jin, Jian-Guo Liu, and Zheng Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206145740396576189},
  year={2017},
}
Shi Jin, Jian-Guo Liu, and Zheng Ma. Uniform spectral convergence of the. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206145740396576189.
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