All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 182

Showing per page

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

Nehla Abdellatif, Christine Bernardi (2004)

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

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.

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

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.

A new quadrilateral MINI-element for Stokes equations

Oh-In Kwon, Chunjae Park (2014)

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

We introduce a new stable MINI-element pair for incompressible Stokes equations on quadrilateral meshes, which uses the smallest number of bubbles for the velocity. The pressure is discretized with the P1-midpoint-edge-continuous elements and each component of the velocity field is done with the standard Q1-conforming elements enriched by one bubble a quadrilateral. The superconvergence in the pressure of the proposed pair is analyzed on uniform rectangular meshes, and tested numerically on uniform...

A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2004)

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

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

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 - Modélisation Mathématique et Analyse Numérique

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,...

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

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,...

A note on the generalized energy inequality in the Navier-Stokes equations

Petr Kučera, Zdeněk Skalák (2003)

Applications of Mathematics

We prove that there exists a suitable weak solution of the Navier-Stokes equation, which satisfies the generalized energy inequality for every nonnegative test function. This improves the famous result on existence of a suitable weak solution which satisfies this inequality for smooth nonnegative test functions with compact support in the space-time.

A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.

Jesús Ildefonso Díaz, Jean-Michel Rakotoson, Paul G. Schmidt (2007)

RACSAM

We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong...

Currently displaying 41 – 60 of 182