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Solving stochastic partial differential equations based on the experimental data
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
2003 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 13, no 3, 415-444 p.Article in journal (Refereed) Published
Abstract [en]

We consider a stochastic linear elliptic boundary value problem whose stochastic coefficient a(x, omega) is expressed by a finite number N-KL of mutually independent random variables, and transform this problem into a deterministic one. We show how to choose a suitable N-KL which should be as low as possible for practical reasons, and we give the a priori estimates for modeling error when a(x, omega) is completely known. When a random function a(x, omega) 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.

Place, publisher, year, edition, pages
2003. Vol. 13, no 3, 415-444 p.
Keyword [en]
covariance, Karhunen Loeve expansion, stationary random function, principle component analysis, identify important factors, large-scale simulations, statistical-analyses, scatterplots, systems
Identifiers
URN: urn:nbn:se:kth:diva-22373ISI: 000181888000009OAI: oai:DiVA.org:kth-22373DiVA: diva2:341071
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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