Solving stochastic partial differential equations based on the experimental data

Ivo Babuška, Kang Man Liu, Raúl Tempone

Research output: Contribution to journalArticle

40 Citations (Scopus)

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

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Stochastic Partial Differential Equations
Partial differential equations
Experimental Data
Modeling Error
Random Function
Elliptic Boundary Value Problems
Independent Random Variables
A Priori Estimates
Error Estimates
Choose
Transform
Random variables
Numerical Results
Boundary value problems
Coefficient
Experiment
Experiments
Model

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

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Solving stochastic partial differential equations based on the experimental data. / Babuška, Ivo; Liu, Kang Man; Tempone, Raúl.

In: Mathematical Models and Methods in Applied Sciences, Vol. 13, No. 3, 01.03.2003, p. 415-444.

Research output: Contribution to journalArticle

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