Journal of Scientific Computing

, Volume 67, Issue 3, pp 1198–1218 | Cite as

A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs



We propose a generalized polynomial chaos based stochastic Galerkin methods for scalar hyperbolic balance laws with random geometric source terms or random initial data. This method is well-balanced (WB), in the sense that it captures the stochastic steady state solution with high order accuracy. The framework of the stochastic WB schemes is presented in details, along with several numerical examples to illustrate their accuracy and effectiveness. The goal of this paper is to show that the stochastic WB scheme yields a more accurate numerical solution at steady state than the non-WB ones.


Uncertainty quantification Hyperbolic balance laws  Well-balanced schemes Generalized polynomial chaos Stochastic Galerkin 



S. Jin was partially supported by NSF DMS Grants Nos. 1107291 and 1107291: RNMS ”KI-Net”, and National Science Foundation of China Grant No. 91330203. D. Xiu was partially supported by AFOSR and DOE.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of Mathematics, Institute of Natural Sciences and MOE-LSCShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Scientific Computing and Imagining Institute and Department of MathematicsUniversity of UtahSalt Lake CityUSA
  4. 4.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA

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