Variational formulation with error estimates for uncertainty quantification via collocation, regression, and sprectral projection

Variational formulation with error estimates for uncertainty quantification via collocation,... Many real world problems need simplifications in such a way that computing is reduced for answering specific questions, for example, to quantify uncertainties. Therefore so‐called metamodels or surrogate models are developed which are based on interpolation or approximation methods. In this paper we transform the usual approximation or interpolation problem into a variational form such as it is known from the Finite Element method (FEM). With this variational framework it is possible to derive error estimators, which can be used later on for adaptivity. To compute the coefficients of the metamodel one needs some quadrature rules, which should be related to the given data. A numerical example shows the advantages of our proposed methods. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Variational formulation with error estimates for uncertainty quantification via collocation, regression, and sprectral projection

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710024
Publisher site
See Article on Publisher Site

Abstract

Many real world problems need simplifications in such a way that computing is reduced for answering specific questions, for example, to quantify uncertainties. Therefore so‐called metamodels or surrogate models are developed which are based on interpolation or approximation methods. In this paper we transform the usual approximation or interpolation problem into a variational form such as it is known from the Finite Element method (FEM). With this variational framework it is possible to derive error estimators, which can be used later on for adaptivity. To compute the coefficients of the metamodel one needs some quadrature rules, which should be related to the given data. A numerical example shows the advantages of our proposed methods. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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