# 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 (2011)

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

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topBenhassine, 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 45.4 (2011): 675-696. <http://eudml.org/doc/197521>.

@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},

keywords = {Stokes equations; incompressible fluids; domain decomposition methods; non-overlapping domain
decomposition methods; FETI-DP methods; cross points; non-overlapping domain decomposition methods},

language = {eng},

month = {1},

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/197521},

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

DA - 2011/1//

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; non-overlapping domain decomposition methods

UR - http://eudml.org/doc/197521

ER -

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