Christoph Schwab

Title:  Elliptic PDEs with random field input -- numerical analysis of forward solvers and of goal oriented input learning

Abstract:

Numerical Analysis of gPC FEM for elliptic PDEs in polygonal or polyhedral domains with random field inputs is addressed; the input data is assumed to be a random field that is represented as a (nonlinear transformed) Karhunen Loeve expansion.

Assuming completely known inputs, we present a-priori analysis of the complexity of the deterministic `forward' solve, in dependence on the regularity of the spatial two-point correlation function of the input data.

Adaptive selection of dimension and spectral order of active parameters in the gPC representation of the random field solution of the PDE will be addressed.

The Compressive Sampling of the input field with respect to the response of the sPDE will be addressed.