 
Summary: An invitation to scientific computing
with finite elements
Fran¸cois Alouges and Bertrand Maury
October 3, 2011
2
Chapter 1
Models for incompressible fluids
1.1 NavierStokes equations
1.1.1 A first glance at the equation
The motion of fluids like air or water can be described in some situations by the Navier
Stokes equations
u
t
+ (u · )u = µu  p + f, (1.1)
div u = 0, (1.2)
where > 0 is the (constant) density of the fluid, µ > 0 its viscosity, and f the force per
unit volume applied to the fluid. The unknowns are u = (u1, u2, u3) for the velocity and
p for the pressure of the fluid.
Equation (1.1) represents the balance law (i.e. ma = F), while (1.2) reflects the
