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 the velocity...

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 the...

The LBB condition is well-known to guarantee the stability of a finite
element (FE) velocity - pressure pair in incompressible flow calculations.
To ensure the condition to be satisfied a certain constant should be positive and
mesh-independent. The paper studies the dependence of the LBB condition on the
domain geometry. For model domains such as strips and rings the
substantial dependence of this constant on geometry aspect ratios is observed.
In domains with highly anisotropic substructures...

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