Energy norm a posteriori error estimation for parametric operator equations

Alex Bespalov, C.E. Powell, DJ Silvester

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)
89 Downloads (Pure)

Abstract

Stochastic Galerkin approximation is an increasingly popular approach for the solution of elliptic PDE problems with correlated random data. A typical strategy is to combine conventional (h-)finite element approximation on the spatial domain with spectral (p-)approximation on a finite-dimensional manifold in the (stochastic) parameter domain. The issues involved in a posteriori error analysis of computed solutions are outlined in this paper using an abstract setting of parametric operator equations. A novel energy error estimator that uses a parameter-free part of the underlying differential operator is introduced which effectively exploits the tensor product structure of the approximation space. We prove that our error estimator is reliable and efficient. We also discuss different strategies for enriching the approximation space and prove two-sided estimates of the error reduction for the corresponding enhanced approximations. These give computable estimates of the error reduction that depend only on the problem data and the original approximation.
Original languageEnglish
Pages (from-to)A339-A363
Number of pages25
JournalSIAM Journal on Scientific Computing
Volume36
Issue number2
Early online date13 Mar 2014
DOIs
Publication statusPublished - 2014

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