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Abstract
We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method, and demonstrate numerically its superiority. The asymptotic cost of solving the stochastic problem with the multilevel method is always significantly lower than that of the standard method and grows only proportionally to the cost of solving the deterministic problem in certain circumstances. Numerical calculations demonstrating the effectiveness of the method for one and twodimensional model problems arising in groundwater flow are presented.
Original language  English 

Pages (fromto)  315 
Number of pages  13 
Journal  Computing and Visualization in Science 
Volume  14 
Issue number  3 
DOIs  
Publication status  Published  1 Jan 2011 
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Dive into the research topics of 'Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients'. Together they form a unique fingerprint.Projects
 1 Finished

Multilevel Monte Carlo Methods for Elliptic Problems
Scheichl, R.
Engineering and Physical Sciences Research Council
1/07/11 → 30/06/14
Project: Research council
Equipment

High Performance Computing (HPC) Facility
Steven Chapman (Manager)
University of BathFacility/equipment: Facility