Multilevel Monte Carlo methods for highly heterogeneous media

Authors:
Aretha L. Teckentrup
Affiliations:
University of Bath, Bath, UK
Venue:
Proceedings of the Winter Simulation Conference
Year:
2012

Citing 5
Cited 0

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Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients

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Abstract

We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random coefficient, and extend the analysis to cover also tensor--valued coefficients, as well as point evaluations. Our analysis includes as an example log--normal random coefficients, which are frequently used in applications.