Variational multiscale stabilization and the exponential decay of fine-scale correctors
Variational multiscale stabilization and the exponential decay of fine-scale correctors
Dokument öffnen (14.2MB)Datum der Veröffentlichung
05.2015Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11889
Inhalt
This paper reviews the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor L2 approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering.
Schlagwörter
Test Space, Standard Finite Element, Galerkin Projection, Corrector Problem, Nodal Basis Function
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/978-3-319-41640-3_11Reihe, Nummer
INS Preprints ; 1509Peterseim, Daniel: Variational multiscale stabilization and the exponential decay of fine-scale correctors. In: INS Preprints, 1509.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11889
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11889
@unpublished{handle:20.500.11811/11889,
author = {{Daniel Peterseim}},
title = {Variational multiscale stabilization and the exponential decay of fine-scale correctors},
publisher = {Institut für Numerische Simulation (INS)},
year = 2015,
month = may,
INS Preprints},
volume = 1509,
note = {This paper reviews the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor L2 approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering.},
url = {https://hdl.handle.net/20.500.11811/11889}
}
author = {{Daniel Peterseim}},
title = {Variational multiscale stabilization and the exponential decay of fine-scale correctors},
publisher = {Institut für Numerische Simulation (INS)},
year = 2015,
month = may,
INS Preprints},
volume = 1509,
note = {This paper reviews the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor L2 approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering.},
url = {https://hdl.handle.net/20.500.11811/11889}
}
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