A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem

Hani Benhassine; Abderrahmane Bendali

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 4, page 675-696
  • ISSN: 0764-583X

Abstract

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This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.

How to cite

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Benhassine, Hani, and Bendali, Abderrahmane. "A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.4 (2011): 675-696. <http://eudml.org/doc/273093>.

@article{Benhassine2011,
abstract = {This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.},
author = {Benhassine, Hani, Bendali, Abderrahmane},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Stokes equations; incompressible fluids; domain decomposition methods; non-overlapping domain decomposition methods; FETI-DP methods; cross points},
language = {eng},
number = {4},
pages = {675-696},
publisher = {EDP-Sciences},
title = {A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem},
url = {http://eudml.org/doc/273093},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Benhassine, Hani
AU - Bendali, Abderrahmane
TI - A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 4
SP - 675
EP - 696
AB - This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.
LA - eng
KW - Stokes equations; incompressible fluids; domain decomposition methods; non-overlapping domain decomposition methods; FETI-DP methods; cross points
UR - http://eudml.org/doc/273093
ER -

References

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