Adaptive wavelet methods for elliptic partial differential equations with random operators

Abstract

We apply adaptive wavelet methods to boundary value problems with random coefficients, discretized by wavelets or frames in the spatial domain and tensorized polynomials in the parameter domain. Greedy algorithms control the approximate application of the fully discretized random operator, and the construction of sparse approximations to this operator. We suggest a power iteration for estimating errors induced by sparse approximations of linear operators.