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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 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.
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.
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 -ma potenza sommabile nel cilindro spazio-temporale . Questo risultato non può essere ulteriormente generalizzato al caso , a causa di noti controesempi.
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.
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....
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...
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 belongs to , then the set of all possible singular points of in is at most finite at every time .
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)...
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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