Efficient adaptive stochastic Galerkin methods for parametric operator equations

Alex Bespalov, David Silvester

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
208 Downloads (Pure)


This paper is concerned with the design and implementation of efficient solution algorithms for elliptic PDE problems with correlated random data. The energy orthogonality that is built into stochastic Galerkin approximations is cleverly exploited to give an innovative energy error estimation strategy that utilizes the tensor product structure of the approximation space. An associated error estimator is constructed and shown theoretically and numerically to be an effective mechanism for driving an adaptive refinement process. The codes used in the numerical studies are available online.
Original languageEnglish
Pages (from-to)A2118–A2140
Number of pages23
JournalSIAM Journal on Scientific Computing
Issue number4
Publication statusPublished - 7 Jul 2016


  • stochastic Galerkin methods
  • stochastic finite elements
  • PDEs with random data
  • error estimation
  • a posteriori error analysis
  • adaptive methods
  • parametric operator equations


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