Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

The kinetic energy of a flow is proportional to the square of the L 2 (Ω) norm of the velocity.
Given a sufficient regular velocity field and a velocity finite element space with polynomials …

The contents of this paper is twofold. First, important recent results concerning finite element
methods for convection-dominated problems and incompressible flow problems are …

Inf-sup stable FEM applied to time-dependent incompressible Navier–Stokes flows are
considered. The focus lies on robust estimates for the kinetic and dissipation energies in a …

An improved understanding of the divergence-free constraint for the incompressible Navier–
Stokes equations leads to the observation that a semi-norm and corresponding equivalence …

In this paper, we consider the recently introduced EMAC formulation for the incompressible
Navier–Stokes (NS) equations, which is the only known NS formulation that conserves …

This article presents error bounds for a velocity–pressure segregated POD reduced order
model discretization of the Navier–Stokes equations. The stability is proven in L∞(L 2) and …

In this paper we analyze a finite element method applied to a continuous downscaling data
assimilation algorithm for the numerical approximation of the two-and three-dimensional …

In the present contribution, we propose a novel conforming finite element scheme for the
time-dependent Navier–Stokes equation, which is proven to be both convection quasi …

Proper orthogonal decomposition (POD) stabilized methods for the Navier--Stokes
equations are considered and analyzed. We consider two cases: the case in which the …