Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions

@article{Mishra2012MultilevelMC,
  title={Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions},
  author={Siddhartha Mishra and Christoph Schwab and Jonas Sukys},
  journal={SIAM J. Sci. Comput.},
  year={2012},
  volume={34}
}
The initial data and bottom topography, used as inputs in shallow water models, are prone to uncertainty due to measurement errors. We model this uncertainty statistically in terms of random shallow water equations. We extend the multilevel Monte Carlo (MLMC) algorithm to numerically approximate the random shallow water equations efficiently. The MLMC algorithm is suitably modified to deal with uncertain (and possibly uncorrelated) data on each node of the underlying topography grid by the use… 

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