Boundary procedures for the time-dependent Burgers' equation under uncertainty

Per Pettersson, Jan Nordström, Gianluca Iaccarino

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The Burgers' equation with uncertain initial and boundary conditions is approximated using a Polynomial Chaos Expansion (PCE) approach where the solution is represented as a series of stochastic, orthogonal polynomials. The resulting truncated PCE system is solved using a novel numerical discretization method based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. The resulting PCE solution yields an accurate quantitative description of the stochastic evolution of the system, provided that appropriate boundary conditions are available. The specification of the boundary data is shown to inuence the solution; we will discuss the problematic implications of the lack of precisely characterized boundary data and possible ways of imposing stable and accurate boundary conditions.

Original languageEnglish
Pages (from-to)539-550
Number of pages12
JournalActa Mathematica Scientia
Issue number2
Publication statusPublished - Mar 2010
Externally publishedYes


  • 35R60
  • 60H35
  • 65C30
  • 65L10
  • polynomial chaos
  • stochastic Burgers' equation
  • uncertainty quantification

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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