Galerkin methods for stochastic hyperbolic problems using bi-orthogonal polynomials

Tao Zhou, Tao Tang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)
7 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)274-292
Number of pages19
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - May 2012

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Bi-orthogonal
  • Hyperbolic equation
  • Regularity
  • Stochastic Galerkin methods


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