Convergence rates of sparse tensor discretizations for PDEs with stochastic data

Christoph Schwab, ETH Z├╝rich

Abstract: We review formulation, regularity and approximation of elliptic, parabolic and hyperbolic PDEs with stochastic data. Using a suitable (generalized) polynomial chaos basis, we reformulate the problem as an infinite dimensional deterministic problem. We show that this problem is uniquely solvable, and we prove regularity results for the parametric solution. We deduce convergence rates of polynomial chaos type approximations for these problems, which only depend on the decay rate of stochastic inputs' fluctuations.

The results in the talk are obtained in joint work with
A. Cohen (Paris VI), R.A. DeVore (Texas A&M), V.H. Hoang (Singapore),
R. Andreev and C.J. Gittelson (ETH).