Journal of Scientific Computing

, Volume 51, Issue 2, pp 274–292 | Cite as

Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials

  • Tao Zhou
  • Tao Tang


This work is concerned with scalar transport equations with random transport velocity. We first give some sufficient conditions that can guarantee the solution to be in appropriate random spaces. Then a Galerkin method using bi-orthogonal polynomials is proposed, which decouples the equation in the random spaces, yielding a sequence of uncoupled equations. Under the assumption that the random wave field has a structure of the truncated KL expansion, a principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in the random spaces. By doing this, the total degree of freedom can be reduced significantly. Numerical experiments are carried out to illustrate the efficiency of the proposed method.


Hyperbolic equation Regularity Stochastic Galerkin methods Bi-orthogonal 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Computational Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon TongChina

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