A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case

Alex Bespalov, Feng Xu

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the framework of stochastic Galerkin finite element methods. We perform a posteriori error analysis of Galerkin approximations and derive a reliable and efficient estimate for the energy error in these approximations. Practical versions of this error estimate are discussed and tested numerically for a model problem with non-affine parametric representation of the coefficient. Furthermore, we use the error reduction indicators derived from spatial and parametric error estimators to guide an adaptive solution algorithm for the given parametric PDE problem. The performance of the adaptive algorithm is tested numerically for model problems with two different non-affine parametric representations of the coefficient.
Original languageEnglish
Number of pages20
JournalComputers & Mathematics with Applications
Volume80
Issue number5
Publication statusAccepted/In press - 30 May 2020

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