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Displaying 41 –
60 of
1082
A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the...
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.
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.
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 regularity criterion for strong solutions of the Ericksen-Leslie equations is established in terms of both the pressure and orientation field in homogeneous multiplier spaces.
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...
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...
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,...
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,...
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.
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1082