Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values

Alexandre Janon; Maëlle Nodet; Clémentine Prieur

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 2, page 317-348
  • ISSN: 0764-583X

Abstract

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We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.

How to cite

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Janon, Alexandre, Nodet, Maëlle, and Prieur, Clémentine. "Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 317-348. <http://eudml.org/doc/273144>.

@article{Janon2013,
abstract = {We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.},
author = {Janon, Alexandre, Nodet, Maëlle, Prieur, Clémentine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {reduced-basis methods; parametrized pdes; nonlinear PDEs; Burgers equation; efficient approximate computation; numerical experiments},
language = {eng},
number = {2},
pages = {317-348},
publisher = {EDP-Sciences},
title = {Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values},
url = {http://eudml.org/doc/273144},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Janon, Alexandre
AU - Nodet, Maëlle
AU - Prieur, Clémentine
TI - Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 2
SP - 317
EP - 348
AB - We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
LA - eng
KW - reduced-basis methods; parametrized pdes; nonlinear PDEs; Burgers equation; efficient approximate computation; numerical experiments
UR - http://eudml.org/doc/273144
ER -

References

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