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Displaying 41 –
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179
We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α 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 the...
We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly
improves accuracy in simulations. Standard finite element schemes
for NS-α 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 the...
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.
The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.
We study the textures of smectic-A liquid crystals consisting in curved, but stricdy equidistant lamellae. Assuming translational symmetry, we can generate them from a single curve. The free energy is a non-trivial functional of it. We learn how to derive the equilibrium equation for this curve, when the texture is confined between two parallel plates, which exert a weak anchoring on the orientation of the lamellae, but do not interfere direcdy with their position. Finally, we describe an instability...
We consider the lowest-order Raviart–Thomas mixed finite element
method for second-order elliptic problems on simplicial meshes in
two and three space dimensions. This method produces saddle-point
problems for scalar and flux unknowns. We show how to easily and
locally eliminate the flux unknowns, which implies the equivalence
between this method and a particular multi-point finite volume
scheme, without any approximate numerical integration. The matrix
of the final linear system is sparse, positive...
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