In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity by random...
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
A number of approaches for discretizing partial differential equations with random data
are based on generalized polynomial chaos expansions of random variables. These constitute
generalizations of the polynomial chaos expansions introduced by Norbert Wiener to
expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We
present conditions on such measures which imply mean-square convergence of generalized
polynomial...
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