Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura; Christine Bernardi; Nejmeddine Chorfi

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 40, Issue: 5, page 897-921
  • ISSN: 0764-583X

Abstract

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We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.

How to cite

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Amoura, Karima, Bernardi, Christine, and Chorfi, Nejmeddine. "Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem." ESAIM: Mathematical Modelling and Numerical Analysis 40.5 (2007): 897-921. <http://eudml.org/doc/194340>.

@article{Amoura2007,
abstract = { We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization. },
author = {Amoura, Karima, Bernardi, Christine, Chorfi, Nejmeddine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Stokes problem; vorticity; velocity and pressure formulation; spectral element methods.; variational formulation; optimal error estimates},
language = {eng},
month = {1},
number = {5},
pages = {897-921},
publisher = {EDP Sciences},
title = {Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem},
url = {http://eudml.org/doc/194340},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Amoura, Karima
AU - Bernardi, Christine
AU - Chorfi, Nejmeddine
TI - Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/1//
PB - EDP Sciences
VL - 40
IS - 5
SP - 897
EP - 921
AB - We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.
LA - eng
KW - Stokes problem; vorticity; velocity and pressure formulation; spectral element methods.; variational formulation; optimal error estimates
UR - http://eudml.org/doc/194340
ER -

References

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