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Solving stochastic partial differential equations based on the experimental data
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DOI：10.1142/S021820250300257X.png)
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Abstract
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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.
Keywords:
covariance
Karhunen Loeve expansion
stationary random function
principle component analysis
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