Robust boundary conditions for stochastic incompletely parabolic systems of equations

Markus Wahlsten, Jan Nordström

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier–Stokes equations.

Original languageEnglish
Pages (from-to)192-213
Number of pages22
JournalJournal of Computational Physics
Publication statusPublished - 15 Oct 2018
Externally publishedYes


  • Incompletely parabolic system
  • Initial boundary value problems
  • Robust design
  • Stochastic data
  • Uncertainty quantification
  • Variance reduction

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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