Also th e convergence rate of essentially first order is s uperior to Monte Carlo sampling.

We study a c lass of integrands that arise as solutions of elli ptic PDEs with log-Gaussian coefficients.

In p articular\, we focus on the overall computational cost of the algorithm.

We prove that certain multilevel QMC rules have a consistent accuracy an d computational cost that is essentially of optima l order in terms of the degrees of freedom of the spatial Finite Element

discretization for a r ange of infinite-dimensional priors.

This is j oint work with Christoph Schwab.

Referenc es:

[L. Herrmann\, Ch. Schwab: QMC integratio n for lognormal-parametric\, elliptic PDEs: local supports and product weights\, Numer. Math. 141(1) pp. 63--102\, 2019]\,

[L. Herrmann\, Ch. Sch wab: Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients\, to appear in ESAIM:M2AN]\,

[L. Herrmann: Strong convergence analysis of iterativ e solvers for random operator equations\, SAM repo rt\, 2017-35\, in review] LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR