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

Loading next page...
 
/lp/wiley/variational-formulation-with-error-estimates-for-uncertainty-00wJE0z1Q8
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off