Various realizations of variational multiscale (VMS) methods for simulating turbulent
incompressible flows have been proposed in the past fifteen years. All of these realizations …

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 …

This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

This paper studies inf-sup stable finite element discretizations of the evolutionary Navier–
Stokes equations with a grad-div type stabilization. The analysis covers both the case in …

In this article, we consider exactly divergence-free H (div)-conforming finite element methods
for time-dependent incompressible viscous flow problems. This is an extension of previous …

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 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 …

A new type of low-regularity integrator is proposed for the Navier--Stokes equations. Unlike
the other low-regularity integrators for nonlinear dispersive equations, which are all fully …

Abstract Two-dimensional Kelvin–Helmholtz instability problems are popular examples for
assessing discretizations for incompressible flows at high Reynolds number. Unfortunately …