<h1>Results</h1>

This is what the program outputs:
@code
Using mapping with degree 1:
============================
cells  |u|_1    error
    5 0.680402 0.572912
   20 1.088141 0.165173
   80 1.210142 0.043172
  320 1.242375 0.010939
 1280 1.250569 0.002745
 5120 1.252627 0.000687

Using mapping with degree 2:
============================
cells  |u|_1    error
    5 1.177062 0.076252
   20 1.228978 0.024336
   80 1.245175 0.008139
  320 1.250881 0.002433
 1280 1.252646 0.000668
 5120 1.253139 0.000175

Using mapping with degree 3:
============================
cells  |u|_1    error
    5 1.193493 0.059821
   20 1.229825 0.023489
   80 1.245221 0.008094
  320 1.250884 0.002430
 1280 1.252646 0.000668
 5120 1.253139 0.000175
@endcode
As we expected, the convergence order for each of the different
mappings is clearly quadratic in the mesh size. What <em>is</em>
interesting, though, is that the error for a bilinear mapping
(i.e. degree 1) is more than three times larger than that for the
higher order mappings; it is therefore clearly advantageous in this
case to use a higher order mapping, not because it improves the order
of convergence but just to reduce the constant before the convergence
order. On the other hand, using a cubic mapping only improves the
result further insignificantly, except for the case of very coarse
grids.
