## Seminar in Numerical Analysis: Oliver Ernst (Technische Universität Bergakademie Freiberg)

**Probabilistic UQ for PDEs with Random Data: A Case Study**

We present a case study for probabilistic uncertainty quantification (UQ) applied to groundwater flow in the context of site assessment for radioactive waste disposal based on data from the Waste Isolation Pilot Plant (WIPP) in Carlsbad, New Mexico. In this context, the primary quantity of interest is the time it takes for a particle of radioactivity to be transported with the groundwater from the repository to man's environment. The mathematical model consists of a stationary diffusion equation for the hydraulic head in which the hydraulic conductivity coefficient is a random field. Once the (stochastic) hydraulic head is computed, contaminant transport can be modelled by particle tracing in the associated velocity field.

We compare two approaches: Gaussian process emulators and stochastic collocation combined with geostatistical techniques for determining the parameters of the input random field's probability law. The second approach involves the numerical solution of the PDE with random data as a parametrized deterministic system. The calculation of the statistics of the travel time from the solution of the stochastic model is formulated for each of the methods being studied and the results compared.

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