Summary
Partial differential equations (PDEs) are key tools in the mathematical modelling of physical processes in science and engineering. Traditional deterministic PDEbased models assume precise knowledge of all inputs (material properties, initial conditions, external forces, etc.). There exist an abundance of numerical methods that can be used to compute a solution to such models to any required accuracy. In practical applications, however, a complete characterisation of all the inputs to a PDE model may not be available. Examples include the modulus of elasticity of a stressed body (in linear elasticity models)and wave characteristics of inhomogeneous media (in wave propagation models). In these cases, simulations based on deterministic models are unable to estimate probabilities of undesirable events (e.g., the fracture of a stressed plate) and, hence, to perform a reliable risk assessment. The emergent area of uncertainty quantification (UQ) deals with mathematical modelling at a different level. It involves the use of probabilistic techniques in order to (i) determine and quantify uncertainties in the inputs to PDEbased models, and (ii) analyse how these uncertainties propagate to the outputs (either the solution to the PDE, or a quantity of interest derived from the solution). The models are then described by PDEs with random data, where both inputs and outputs take the form of random fields ... more
The project builds on the research in the precursor project
Analysis of Numerical Methods for Partial Differential Equations with Random Data
Research outputs to date

Efficient Adaptive Algorithms for Elliptic PDEs with Random Data, SIAM/ASA J. Uncertainty Quantification, 6(1), 243272, 2017

CBS constants and their role in error estimation for stochastic Galerkin finite element methods,
Journal of Scientific Computing, 2018

Collocation methods for exploring perturbations
in linear stability analysis,
SIAM J. on Scientific Computing, 40(4), A2667A2693, 2018

Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity,
arXiv:1710.03328, 2018

Goaloriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs,
arXiv:1806.03928, 2018

Robust preconditioning for stochastic Galerkin formulations of parameterdependent linear elasticity equations,
arXiv:1803.01572, 2018

Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation,
arXiv:1806.05987, 2018
Research software

SIFISS
solves diffusion problems with uncertain coefficients (square domain, needs
IFISS)

Stochastic TIFISS
solves diffusion problems with uncertain coefficients (aribtrary twodimensional domains)
Page last modified: 21 September 2018