Mathematics

We discuss parametrizations of random coefficiens for PDEs based on Karhunen-Loeve, Haar and other series  expansions. Theoretically, these coefficients are properly described only if an infinite number of terms (random variables) is used. Practically only a few terms are needed to describe the random coefficients with sufficient accuracy. Thus, it is reasonable to limit the analysis to just a few random variables in the expansion.

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We consider stochastic collocation method consisting of a Galerkin approximation in space and a collocation in the zeros of appropriate orthogonal polynomials in the probability space.