Finite Element Methods for Flow Problems
Incompressible Flow  
  Steady Transport
  Unsteady Transport
  Compressible Flow
  Unsteady Convection-Diffusion
  Incompressible Flow
Ex 1: Analytical Stokes
Ex 2: Cavity flow
Ex 3: Plane jet simulation
Here we analyze Navier-Stokes equations, which govern the behavior of viscous incompressible flows:
These equations can be rewritten in a dimensionless form:
where is known as the flow Reynolds number.

Solving these equations shows mainly two difficulties:
  Nonlinear convective terms
  Stabilized formulations have to be used to ensure a stable solution when dealing with high Reynolds number flows.
  Incompressibility constraint
  The unknowns (velocity and pressure) cannot be discretized anyhow. Solution is guaranteed if interpolation spaces verify a stability condition known as inf-sup or LBB condition.
Besides, when the unsteady case is considered, we have to find proper techniques to trace the transient solution.

Examples on incompressible flow problems
 Stokes problem with analytical solution
 Cavity flow problem
 Plane jet simulation

 Unsteady Convection-Diffusion