Efficient adaptive algorithms for elliptic PDEs with random data

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Abstract

We present a novel adaptive algorithm implementing the stochastic Galerkin finite element method for numerical solution of elliptic PDE problems with correlated random data. The algorithm employs a hierarchical a posteriori error estimation strategy which also provides effective estimates of the error reduction for enhanced approximations. These error reduction indicators are used in the algorithm to perform a balanced adaptive refinement of spatial and parametric components of Galerkin approximations. The results of numerical tests demonstrating the efficiency of the algorithm for three representative PDEs with random coefficients are reported.
The software used for numerical experiments is available online.

Details

Original languageEnglish
Pages (from-to)243–272
JournalSIAM/ASA Journal on Uncertainty Quantification
Volume6
Issue number1
Early online date6 Mar 2018
Publication statusPublished - 2018

Keywords

  • stochastic Galerkin methods , stochastic finite elements, PDEs with random data , adaptive methods , a posteriori error estimation, singularities , parametric PDEs