A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
View/Date of Publication
12.2020Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11795
Abstract
We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and time-discretization-errors in our consideration. Numerical experiments illustrate our results.
Subjects
Quasilinear parabolic partial differential equation, Reduced basis, Proper Orthogonal Decomposition, A-posteriori error
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s10589-021-00299-yPart of Series
INS Preprints ; 2005Hoppe, Fabian; Neitzel, Ira: A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE. In: INS Preprints, 2005.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11795
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11795
@unpublished{handle:20.500.11811/11795,
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = dec,
INS Preprints},
volume = 2005,
note = {We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and time-discretization-errors in our consideration. Numerical experiments illustrate our results.},
url = {https://hdl.handle.net/20.500.11811/11795}
}
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = dec,
INS Preprints},
volume = 2005,
note = {We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and time-discretization-errors in our consideration. Numerical experiments illustrate our results.},
url = {https://hdl.handle.net/20.500.11811/11795}
}
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