Link to the source code for this example:

The console output of the program:

***************************************************************
* Running Example vector_fe_ex5:
*   ./example-opt
***************************************************************

Running /home/jwpeterson/software/libmesh_build/opt_real/examples/vector_fe/vector_fe_ex5/.libs/example-opt

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=256
    n_local_nodes()=256
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "Poisson"
    Type "NonlinearImplicit"
    Variables="u"
    Finite Element Types="MONOMIAL_VEC"
    Approximation Orders="FIRST"
    n_dofs()=1350
    n_local_dofs()=1350
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 28.4
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 30
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
      Number of Node Constraints = 0

  NL step  0, |residual|_2 = 4.005729e+01
  NL step  1, |residual|_2 = 2.899288e-04
  NL step  2, |residual|_2 = 2.110835e-09

***************************************************************
* Done Running Example vector_fe_ex5:
*   ./example-opt
***************************************************************