Solving stochastic partial differential equations based on the experimental data

Ivo Babuška*, Kang Man Liu, Raul Tempone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We consider a stochastic linear elliptic boundary value problem whose stochastic coefficient a(x, w) is expressed by a finite number NKL of mutually independent random variables, and transform this problem into a deterministic one. We show how to choose a suitable NKL which should be as low as possible for practical reasons, and we give the a priori estimates for modeling error when a(x, w) is completely known. When a random function a(x, w) is selected to fit the experimental data, we address the estimation of the error in this selection due to insufficient experimental data. We present a simple model problem, simulate the experiments, and give the numerical results and error estimates.

Original languageEnglish (US)
Pages (from-to)415-444
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume13
Issue number3
DOIs
StatePublished - Mar 1 2003

Keywords

  • Covariance
  • Karhunen Loeve expansion
  • Principle component analysis
  • Stationary random function

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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