Sparse adaptive tensor discretizations of nonlinear operator equations with random parameters
We consider a class of nonlinear, Frechet-differentiable operator equations with random inputs. We establish local solvability of these equations and present a first order, second moment analysis of the random solutions, based on a suitable version of the implicit function theorem. We derive a deterministic tensorized operator equation for the first order approximation of the k-point correlation function of the random solution. We establish its well-posedness and a regularity result in scales of anisotropic Sobolev and Besov spaces. Sparse tensor Galerkin discretizations are proved to converge at rates independent of k; the proposed algorithms do not require formation of the tensorized matrix. Examples include first kind boundary integral equations for parabolic evolution problems in domains with random boundary surfaces Show more
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PublisherSchool of Mathematics and Statistics, University of New South Wales
Organisational unit03435 - Schwab, Christoph
NotesInvited Talk on 8 November 2011.
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