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Journal of Scientific Computing

Erschienen in:

01.06.2013

Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework

verfasst von: Yanlai Chen, Sigal Gottlieb

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2013

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Abstract

In this paper, we present the first reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced Collocation Method (ERCM). This work provides a reduced basis strategy to practitioners who prefer a collocation, rather than Galerkin, approach. Furthermore, the empirical reduced collocation method eliminates a potentially costly online procedure that is needed for non-affine problems with Galerkin approach. Numerical results demonstrate the high efficiency and accuracy of the reduced collocation methods, which match or exceed that of the traditional reduced basis method in the Galerkin framework.

Vorheriger Artikel Numerical Modeling of Degenerate Equations in Porous Media Flow

Nächster Artikel An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations

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Titel: Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework
verfasst von: Yanlai Chen
Sigal Gottlieb
Publikationsdatum: 01.06.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9654-z

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