Reduced Basis Methods for PDEs with Random Inputs

Craig Newsum (The University of Manchester)

ATB Frank Adams 1,

In this talk, we begin by introducing uncertainty quantification (UQ) and then give an overview of some stochastic finite element methods for the forward propagation of uncertainty in PDEs, specifically stochastic collocation methods (SCMs). We then describe our research on reduced basis methods (RBMs), which can be combined with SCMs to perform UQ more cheaply. In particular, we develop an efficient RBM for a groundwater flow model with uncertain permeability coefficient and present numerical experiments which demonstrate the efficiency of our approach over standard finite element methods.

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