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Boundary Conditions and Data

  • Mass Per Pettersson
  • Gianluca Iaccarino
  • Jan Nordström
Chapter
  • 2k Downloads
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

We continue analysis of Burgers’ equation from the previous chapter with a focus on the effect of data for the boundary conditions. To facilitate understanding, we deal only with the truncated representation \(u(x,t,\xi ) = u_{0}\psi _{0} + u_{1}\psi _{1}\). This means that all the stochastic variation is accounted for by the single gPC coefficient u 1, and the standard deviation of the solution is simply | u 1 | . With this simplified setup, we obtain a few combinations of general situations for the boundary data: known expectation but unknown standard deviation, unknown expectation and standard deviation, etc. The implication in all these situations on well-posedness, stability and accuracy is discussed.

Keywords

Unknown Standard Deviation Boundary Data Unknown Expectation Simple Apparatus Stochastic Variables 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reference

  1. 1.
    Pettersson P, Iaccarino G, Nordström J (2010) Boundary procedures for the time-dependent Burgers’ equation under uncertainty. Acta Math Sci 30(2):539–550. doi: 10.1016/S0252-9602(10)60061-6, http://www.sciencedirect.com/science/article/pii/S0252960210600616

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mass Per Pettersson
    • 1
  • Gianluca Iaccarino
    • 2
  • Jan Nordström
    • 3
  1. 1.Uni ResearchBergenNorway
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mathematics Computational MathematicsLinköping UniversityLinköpingSweden

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