Solving stochastic partial differential equations based on the experimental data

We consider a stochastic linear elliptic boundary value problem whose stochastic coefficient a(x, w) 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, 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.