On a C 0 Semigroup Associated with a Modified Oseen Equation with Rotating Effect

AbstractBased on the relaxed factorization techniques studied recently and the idea of the simple-like preconditioner, a modified relaxed positive-semidefinite and skew-Hermitian splitting (MRPSS) preconditioner is proposed for generalized saddle point problems. Some properties, including the eigenvalue distribution, the eigenvector distribution and the minimal polynomial of the preconditioned matrix are studied. Numerical examples arising from the mixed finite element discretization of the Oseen equation are illustrated to show the efficiency of the new preconditioner.

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Least-squares method for the Oseen equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22055 ◽

2016 ◽

Vol 32 (4) ◽

pp. 1289-1303 ◽

Cited By ~ 2

Author(s):

Zhiqiang Cai ◽

Binghe Chen

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Oseen Equation

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The internal stabilization of the Stokes–Oseen equation by feedback point controllers

Systems & Control Letters ◽

10.1016/j.sysconle.2013.02.009 ◽

2013 ◽

Vol 62 (5) ◽

pp. 447-450

Author(s):

Viorel Barbu

Keyword(s):

Oseen Equation ◽

Internal Stabilization

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Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2017031 ◽

2018 ◽

Vol 52 (1) ◽

pp. 99-122

Author(s):

Gabriel R. Barrenechea ◽

Andreas Wachtel

Keyword(s):

Finite Element ◽

Aspect Ratio ◽

Error Estimates ◽

Finite Element Methods ◽

A Priori ◽

Oseen Equation ◽

Quadrilateral Meshes ◽

Oseen Problem ◽

Two Space Dimensions ◽

Element Pair

In this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order ℚ12 × ℙ0 pair, we first identify the pressure components that make this finite element pair to be non-inf-sup stable, especially with respect to the aspect ratio. We then propose a way to penalise them, both strongly, by directly removing them from the space, and weakly, by adding a stabilisation term based on jumps of the pressure across selected edges. Concerning the velocity stabilisation, we propose an enhanced grad-div term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically.

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