### 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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Title of host publication | International Conference on Computational Methods in Water Resources, CMWR |

Editors | V.N. Burganos, G.P. Karatzas, A.C. Payatakes, C.A. Brebbia, W.G. Gray, G.F. Pinder |

Publisher | Computational Mechanics Publ |

Pages | 347-354 |

Number of pages | 8 |

Volume | 1 |

State | Published - 1998 |

Externally published | Yes |

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 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*International Conference on Computational Methods in Water Resources, CMWR*(Vol. 1, pp. 347-354). Computational Mechanics Publ.

**Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements.** / Guadagnini, A.; Neuman, Shlomo P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*International Conference on Computational Methods in Water Resources, CMWR.*vol. 1, Computational Mechanics Publ, pp. 347-354, Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2), Crete, Greece, 6/1/98.

}

TY - GEN

T1 - Deterministic solution of stochastic groundwater flow equations by nonlocal finite elements

AU - Guadagnini, A.

AU - Neuman, Shlomo P

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031699838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031699838&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0031699838

VL - 1

SP - 347

EP - 354

BT - International Conference on Computational Methods in Water Resources, CMWR

A2 - Burganos, V.N.

A2 - Karatzas, G.P.

A2 - Payatakes, A.C.

A2 - Brebbia, C.A.

A2 - Gray, W.G.

A2 - Pinder, G.F.

PB - Computational Mechanics Publ

ER -