On the approximation of the spectrum of the Stokes operator

Geveci, Tunc; Reddy, B. D.; Pearce, H. T.

doi:10.1051/m2an/1989230101291

Cited by 3 publications

(4 citation statements)

References 10 publications

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“…We have obtained an error

\underset{max}{msub} MathClass-rel| λ_{i} MathClass-bin- λ_{i}^{ϵ} MathClass-rel|

that decreases linearly as O ( ϵ ) (see for more details). This error is similar to the one obtained for the Stokes operator by Geveci et al in . We mention that we have obtained the same behavior of this error as a function of δ with ϵ = 0.…”

Section: Numerical Resultssupporting

confidence: 91%

A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation

Amodei

Buchot

2011

Numerical Linear Algebra App

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“…We have obtained an error

\underset{max}{msub} MathClass-rel| λ_{i} MathClass-bin- λ_{i}^{ϵ} MathClass-rel|

Section: Numerical Resultssupporting

confidence: 91%

A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation

Amodei

Buchot

2011

Numerical Linear Algebra App

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“…We have the following result: Proof. The arguments in [8] can be followed exactly in our case. Indeed, the proofs therein are based on estimates like (7.1) and (7.2) and on the fact that |λ hj and by using Theorem 7.1 and (6.8) we conclude the theorem by passing to the limit as h → 0.…”

Section: Cpmentioning

confidence: 79%

“…To analyze the asympotic behavior of our problem, we are going to use the arguments in [8]. In that paper a different problem is considered: the Stokes one and a regularized (or penalized) version of it.…”

Section: Asymptotic Behavior For C → ∞mentioning

confidence: 99%

Finite element analysis of compressible and incompressible fluid-solid systems

Bermúdez¹,

Durán²,

Rodrı́guez³

1998

Math. Comp.

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Abstract. This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a nonconforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and error estimates independent of the acoustic speed are given. For incompressible fluids, a convenient equivalent stream function formulation and a post-process to compute the pressure are introduced.

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“…. .. Methods for solving Stokes eigenvalue problems numerically are outlined in, for example, [6,23]. Let (f, g) t denote the L 2 (V F (t)) inner product of f and g and…”

Section: Spectral Basismentioning

confidence: 99%