Stochastic finite elements: Computational approaches to stochastic partial differential equations

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 on uncertain systems, where the randomness is assumed spatial. Traditional computational approaches usually use some form of perturbation or Monte Carlo simulation. This is contrasted here with more recent methods based on stochastic Galerkin approximations. Also some approaches to an adaptive uncertainty quantification are pointed out. {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 on uncertain systems, where the randomness is assumed spatial. Traditional computational approaches usually use some form of perturbation or Monte Carlo simulation. This is contrasted here with more recent methods based on stochastic Galerkin approximations. Also some approaches to an adaptive uncertainty quantification are pointed out.}