Adaptivity and variational stabilization for convection-diffusion equations

Albert Cohen; Wolfgang Dahmen; Gerrit Welper

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2012)

  • Volume: 46, Issue: 5, page 1247-1273
  • ISSN: 0764-583X

Abstract

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In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies, based on other specifications, are explored and illustrated by numerical experiments.

How to cite

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Cohen, Albert, Dahmen, Wolfgang, and Welper, Gerrit. "Adaptivity and variational stabilization for convection-diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.5 (2012): 1247-1273. <http://eudml.org/doc/273263>.

@article{Cohen2012,
abstract = {In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies, based on other specifications, are explored and illustrated by numerical experiments.},
author = {Cohen, Albert, Dahmen, Wolfgang, Welper, Gerrit},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {variational problems; adaptivity; a-posteriori error estimators; stabilization; a posteriori error estimators; convection-diffusion problems; numerical experiments},
language = {eng},
number = {5},
pages = {1247-1273},
publisher = {EDP-Sciences},
title = {Adaptivity and variational stabilization for convection-diffusion equations},
url = {http://eudml.org/doc/273263},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Cohen, Albert
AU - Dahmen, Wolfgang
AU - Welper, Gerrit
TI - Adaptivity and variational stabilization for convection-diffusion equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 5
SP - 1247
EP - 1273
AB - In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies, based on other specifications, are explored and illustrated by numerical experiments.
LA - eng
KW - variational problems; adaptivity; a-posteriori error estimators; stabilization; a posteriori error estimators; convection-diffusion problems; numerical experiments
UR - http://eudml.org/doc/273263
ER -

References

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