A multilevel adaptive refinement strategy for solving linear elliptic partial differential
equations with random data is recalled in this work. The strategy extends the a posteriori …

Error control by means of a posteriori error estimators or indica-tors and adaptive
discretizations, such as adaptive mesh refinement, have emerged in the late seventies …

We present an adaptive algorithm for the computation of quantities of interest involving the
solution of a stochastic elliptic partial differential equation, where the diffusion coefficient is …

We present an adaptive algorithm for the computation of quantities of interest involving the
solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means …

Physical models with uncertain inputs are commonly represented as parametric partial
differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of …

We propose and analyze a general goal-oriented adaptive strategy for approximating
quantities of interest (QoIs) associated with solutions to linear elliptic partial differential …

This paper is focused on the convergence analysis of an adaptive stochastic collocation
algorithm for the stationary diffusion equation with parametric coefficient. The algorithm …

We investigate the use of a class of quasi-Monte Carlo (QMC) quadrature rules, called
Extrapolated Polynomial Lattices, to approximate expected values of quantities of interest …

Partial differential equations (PDEs) are used to model many processes in science and
engineering. In this work we are particularly interested in evolutionary problems modelled …