A number of approaches for discretizing partial differential equations with random data are
based on generalized polynomial chaos expansions of random variables. These constitute …

The series aims to: present current and emerging innovations in GIScience; describe new
and robust GIScience methods for use in transdisciplinary problem solving and decision …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

The numerical solution of optimization problems governed by partial differential equations
(PDEs) with random coefficients is computationally challenging because of the large number …

Uncertainty is inevitable when solving science and engineering application problems. In the
face of uncertainty, it is essential to determine robust and risk-averse solutions. In this work …

We describe the analysis and the implementation of two finite element (FE) algorithms for
the deterministic numerical solution of elliptic boundary value problems with stochastic …

We propose and analyze sparse deterministic-stochastic tensor Galerkin finite element
methods (sparse sGFEMs) for the numerical solution of elliptic partial differential equations …

COMPUTATIONAL fluid dynamics (CFD) has evolved considerably since emerging in the
1960s, tracking improvements in computational hardware and algorithm development. CFD …

In technical applications, uncertainties are a topic of increasing interest. During the last
years the Polynomial Chaos of Wiener (Amer. J. Math. 60 (4), 897–936, 1938) was revealed …

Uncertainty estimation arises at least implicitly in any kind of modelling of the real world, and
it is desirable to actually quantify the uncertainty in probabilistic terms. Here the emphasis is …