Adaptive stochastic Galerkin methods: beyond the elliptic case

Abstract

We derive an adaptive solver for random boundary value problems, building on adaptive wavelet algorithms for non-elliptic problems. Replacing wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which may be combined with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations, including a comparison of various adaptive methods.