Solving stochastic partial differential equations based on the experimental data
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
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.
covariance, Karhunen Loeve expansion, stationary random function, principle component analysis, identify important factors, large-scale simulations, statistical-analyses, scatterplots, systems
IdentifiersURN: urn:nbn:se:kth:diva-22373ISI: 000181888000009OAI: oai:DiVA.org:kth-22373DiVA: diva2:341071
QC 201005252010-08-102010-08-10Bibliographically approved