We analyze the ensemble and polynomial chaos Kalman filters applied to nonlinear
stationary Bayesian inverse problems. In a sequential data assimilation setting, such …

The discretization of linear partial differential equations with random data by means of the
stochastic Galerkin finite element method results in general in a large coupled linear system …

In this article, we describe an efficient approximation of the stochastic Galerkin matrix which
stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed …

Stochastic Galerkin methods for non-affine coefficient representations are known to cause
major difficulties from theoretical and numerical points of view. In this work, an adaptive …

This work is concerned with the development and study of a minimum residual norm
subspace method based on the generalized conjugate residual method with inner …

We provide a brief introduction to Bayesian inverse problems and Bayesian estimators
emphasizing their similarities and differences to the classical regularized least-squares …

This work is concerned with the propagation of uncertainty across coupled domain problems
with high-dimensional random inputs. A stochastic model reduction approach based on low …

Presented here is a finite element framework for the solution of stochastic elastoplastic
boundary value problems with non-Gaussian parametric uncertainty. The framework relies …

In this paper the irreversible behaviour of solids and structures in terms of rate-independent
elastoplastic constitutive models in the presence of uncertainty in both material description …

In this work a general approach to compute a compressed representation of the exponential
exp (h) of a high-dimensional function h is presented. Such exponential functions play an …