### Abstract

We consider the effect of measuring randomly varying hydraulic conductivities K(x) on the prediction of groundwater flow in a bounded porous domain under uncertainty. Hydraulic head is governed by a stochastic Poisson equation subject to random source and boundary terms. We present a system of exact nonlocal deterministic equations for optimum unbiased predictors of these quantities and for measures of corresponding prediction errors. We then develop recursive approximations for these equations and solve them to leading order in the variance of ln K(x) by nonlocal Galerkin finite elements. Our results compare well with Monte Carlo simulations of mean uniform and convergent flows in media with large variance and arbitrary correlation.

Original language | English (US) |
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Pages | 347-354 |

Number of pages | 8 |

State | Published - Jan 1 1998 |

Event | Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) - Crete, Greece Duration: Jun 1 1998 → Jun 1 1998 |

### Other

Other | Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) |
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City | Crete, Greece |

Period | 6/1/98 → 6/1/98 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements*. 347-354. Paper presented at Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2), Crete, Greece, .