Displaying similar documents to “A penalty algorithm for the spectral element discretization of the Stokes problem*”

A penalty algorithm for the spectral element discretization of the Stokes problem

Christine Bernardi, Adel Blouza, Nejmeddine Chorfi, Nizar Kharrat (2011)

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

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The penalty method when applied to the Stokes problem provides a very efficient algorithm for solving any discretization of this problem since it gives rise to a system of two equations where the unknowns are uncoupled. For a spectral or spectral element discretization of the Stokes problem, we prove estimates that allow us to optimize the penalty parameter as a function of the discretization parameter. Numerical experiments confirm the interest of this technique.

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

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

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

Hani Benhassine, Abderrahmane Bendali (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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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....

Enabling numerical accuracy of Navier-Stokes- through deconvolution and enhanced stability

Carolina C. Manica, Monika Neda, Maxim Olshanskii, Leo G. Rebholz (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS- suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on...

A new formulation of the Stokes problem in a cylinder, and its spectral discretization

Nehla Abdellatif, Christine Bernardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.