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# Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

@inproceedings{Todor2007ConvergenceRF, title={Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients}, author={Radu Alexandru Todor and Christoph Schwab}, year={2007} }

- Published 2007

A scalar, elliptic boundary-value problem in divergence form with stochastic diffusion coefficient a(x, ω) in a bounded domain D ⊂ Rd is reformulated as a deterministic, infinite-dimensional, parametric problem by separation of deterministic (x ∈ D) and stochastic (ω ∈ Ω) variables in a(x, ω) via Karhúnen–Loève or Legendre expansions of the diffusion coefficient. Deterministic, approximate solvers are obtained by projection of this problem into a product probability space of finite dimension M… CONTINUE READING