4 papers
Optimized multilevel Monte Carlo methods in Banach spaces
Kristin Kirchner, Fabio Nobile, Christoph Schwab +1
We present a theoretical and numerical analysis of Monte Carlo methods for the estimation of statistical moments of random variables taking values in a Banach sp…
Elliptic PDEs on log-Gaussian Shapes: Sparsity and Finite Element Discretization
Dinh Dũng, Helmut Harbrecht, Van Kien Nguyen +1
In this article, we consider the solution to elliptic diffusion problems on a class of random domains obtained by log-Gaussian random homothety of the unit disk respectively an ann…
Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation
U. Koley, N. H. Risebro, Ch. Schwab +1
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recen…
Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients
Frances Y. Kuo, Christoph Schwab, Ian H. Sloan
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estim…