Kolloquiumsvortrag, Prof. Dr. Helmut Harbrecht, Universität Basel / am 02.06.2017
Ludewig-Meyn-Str. 2, Raum Ü2/K (LMS2, R. Ü2/K)
Titel: On multilevel quadrature for elliptic partial differential equations with random input
This talk is dedicated to multilevel quadrature methods for the rapid solution of partial differential equations with a random input parameter. The key idea of such approaches is a sparse-grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution’s moments with focus on the mean and the variance in case of second order elliptic boundary value problems with random diffusion. In particular, the present framework covers the multilevel Monte Carlo method and the multilevel quasi-Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments.