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A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces...

A uniqueness criterion for the solution of the stationary Navier-Stokes equations

Giovanni Prouse (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A uniqueness criterion is given for the weak solution of the Navier-Stokes equations in the stationary case. Precisely, it is proved that, for a generic known term, there exists one and only one solution such that the mechanical power of the corresponding flow is maximum and that this maximum is "stable" in an appropriate sense.

A uniqueness theorem for the approximable solutions of the stationary Navier-Stokes equations

Giovanni Prouse (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is proved that there can exist at most one solution of the homogeneous Dirichlet problem for the stationary Navier-Stokes equations in 3-dimensional space which is approximable by a given consistent and regular approximation scheme.

A uniqueness theorem for viscous flows on exterior domains with summability assumptions on the gradient of pressure.

Giovanni P. Galdi, Paolo Maremonti (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota si fornisce un teorema di unicità per soluzioni regolari delle equazioni di Navier-Stokes in domini esterni. Tale teorema non richiede che le velocità tendano ad un prefissato limite all'infinito, mentre il gradiente di pressione è supposto essere di q -ma potenza sommabile nel cilindro spazio-temporale ( q ∈ ( 1 , ∞ ) ) . Questo risultato non può essere ulteriormente generalizzato al caso q = ∞ , a causa di noti controesempi.

About the decay of surface waves on viscous fluids without surface tension

Gerhard Ströhmer (2003)

Banach Center Publications

We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.

Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

Simone Deparis, Miguel Angel Fernández, Luca Formaggia (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure....

Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

Simone Deparis, Miguel Angel Fernández, Luca Formaggia (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of...

Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class L ∞ ( 0 , T , L 3 ( Ω ) 3 )

Zdeněk Skalák (2003)

Applications of Mathematics

We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution 𝐮 belongs to L ∞ ( 0 , T , L 3 ( Ω ) 3 ) , then the set of all possible singular points of 𝐮 in Ω is at most finite at every time t 0 ∈ ( 0 , T ) .

An application of the BDDC method to the Navier-Stokes equations in 3-D cavity

Hanek, Martin, Šístek, Jakub, Burda, Pavel (2015)

Programs and Algorithms of Numerical Mathematics

We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab)...

An error estimate uniform in time for spectral Galerkin approximations for the equations for the motion of a chemical active fluid.

M. A. Rojas-Medar, S. A. Lorca (1995)

Revista Matemática de la Universidad Complutense de Madrid

We study error estimates and their convergence rates for approximate solutions of spectral Galerkin type for the equations for the motion of a viscous chemical active fluid in a bounded domain. We find error estimates that are uniform in time and also optimal in the L2-norm and H1-norm. New estimates in the H(-1)-norm are given.

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