Sparse second moment analysis for elliptic problems in stochastic domains

@article{Harbrecht2008SparseSM,
  title={Sparse second moment analysis for elliptic problems in stochastic domains},
  author={Helmut Harbrecht and Reinhold Schneider and Christoph Schwab},
  journal={Numerische Mathematik},
  year={2008},
  volume={109},
  pages={385-414}
}
We consider the numerical solution of elliptic boundary value problems in domains with random boundary perturbations. Assuming normal perturbations with small amplitude and known mean field and two-point correlation function, we derive, using a second order shape calculus, deterministic equations for the mean field and the two-point correlation function of the random solution for a model Dirichlet problem which are 3rd order accurate in the boundary perturbation size. Using a variational… CONTINUE READING

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