• A STATIC CONDENSATION REDUCED...

Treffer: A STATIC CONDENSATION REDUCED BASIS ELEMENT METHOD: APPROXIMATION AND A POSTERIORI ERROR ESTIMATION

Title:
A STATIC CONDENSATION REDUCED BASIS ELEMENT METHOD: APPROXIMATION AND A POSTERIORI ERROR ESTIMATION
Authors:
PHUONG HUYNH, Dinh Bao, KNEZEVIC, David J, PATERA, Anthony T
Source:
Modélisation mathématique et analyse numérique (Imprimé). 47(1):213-251
Publisher Information:
Les Ulis: EDP Sciences, 2013.
Publication Year:
2013
Physical Description:
print, 28 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations aux dérivées partielles, problèmes aux valeurs initiales et problèmes aux valeurs limites dépendant du temps, Partial differential equations, initial value problems and time-dependant initial-boundary value problems, Equations aux dérivées partielles, problèmes aux valeurs limites, Partial differential equations, boundary value problems, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse numérique, Numerical analysis, Análisis numérico, Approximation, Aproximación, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation elliptique, Elliptic equation, Ecuación elíptica, Erreur approximation, Approximation error, Error aproximación, Estimation a posteriori, A posteriori estimation, Estimación a posteriori, Estimation erreur, Error estimation, Estimación error, Modèle mathématique, Mathematical model, Modelo matemático, Méthode numérique, Numerical method, Método numérico, Méthode stochastique, Stochastic method, Método estocástico, Méthode élément fini, Finite element method, Método elemento finito, Problème valeur initiale, Initial value problem, Problema valor inicial, Problème valeur limite, Boundary value problem, Problema valor limite, Représentation fonction, Function representation, Representación función, Stabilité numérique, Numerical stability, Estabilidad numérica, Transfert chaleur, Heat transfer, Transferencia térmica, 35Jxx, 35XX, 65C20, 65M99, 65Mxx, 65N99, 65Nxx
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 02139 MA, United States
School of Engineering and Applied Sciences, Harvard University, Cambridge, 02138 MA, United States
ISSN:
0764-583X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26900882
Rights:
Copyright 2014 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.26900882
Database:
PASCAL Archive

Weitere Informationen

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigen-function port representation at the interface level, and finally Reduced Basis (RB) approximation of Finite Element (FE) bubble functions at the intradomain level. We show under suitable hypotheses that the RB Schur complement is close to the FE Schur complement: we can thus demonstrate the stability of the discrete equations; furthermore, we can develop inexpensive and rigorous (system-level) a posteriori error bounds. We present numerical results for model many-parameter heat transfer and elasticity problems with particular emphasis on the Online stage; we discuss flexibility, accuracy, computational performance, and also the effectivity of the a posteriori error bounds.