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Stochastic Galerkin reduced basis methods for parametrized random elliptic PDEs

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      Abstract

      We consider the estimation of parameter-dependent statistical outputs for parametrized elliptic PDE problems with random data. We propose a stochastic Galerkin reduced basis method, which provides the expected output for a given parameter value at the cost of solving a single low-dimensional system of equations. This is substantially faster than usual Monte Carlo reduced basis methods, which require multiple samples of the reduced solution.

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      Affiliations
      [1 ]Technische Universität Darmstadt, Graduate School of Computational Engineering
      [2 ]Technische Universität Darmstadt, Department of Mathematics
      [* ]Correspondence: ullmann@ 123456gsc.tu-darmstadt.de
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      ScienceOpen
      27 April 2018
      10.14293/P2199-8442.1.SOP-MATH.FFVLPM.v1
      Copyright © 2018

      This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

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