Efficient adaptive stochastic Galerkin methods for parametric operator equations

Bespalov, Alex and Silvester, David (2015) Efficient adaptive stochastic Galerkin methods for parametric operator equations. [MIMS Preprint]

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Abstract

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.

Item Type: MIMS Preprint
Uncontrolled Keywords: stochastic Galerkin methods, stochastic finite elements, PDEs with random data, error estimation, a posteriori error analysis, adaptive methods, parametric operator equations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: professor david silvester
Date Deposited: 21 Jun 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2313

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