In Lab 4, Exercise 9, FEM with quadratic shape fns in 1d is used to
solve a Dirichlet BVP on [0,1]: y''+y'+y=x*(1-x).  Mesh is uniform.
Using inf-norm, convergence table is:
  N    h        error      ratio
  7  1.2500e-1 7.2202e-06 15.460
 15  6.2500e-2 4.6703e-07 15.788
 31  3.1250e-2 2.9581e-08 14.013
 61  1.6129e-2 2.1110e-09 14.951
121  8.1967e-3 1.4119e-10

Question: 1.  Why is progression of ratios not better?
          2.  Why is convergence quadratic?  Theory says cubic, but
              mesh is uniform...

Re-wrote code using Fortran.  Re-did convergence table using L2 norm.
   N=           7  err=  2.2508E-05 ratio= 15.854 
   N=          15  err=  1.4197E-06 ratio= 15.963
   N=          31  err=  8.8941E-08 ratio= 14.084
   N=          61  err=  6.3151E-09 ratio= 14.990
   N=         121  err=  4.2128E-10 ratio= 15.481
   N=         241  err=  2.7212E-11 ratio= 15.737
   N=         481  err=  1.7292E-12 ratio= 15.868
   N=         961  err=  1.0897E-13 ratio= 15.934
   N=        1921  err=  6.8395E-15 ratio= 15.967
   N=        3841  err=  4.2836E-16 ratio= 15.983
   N=        7681  err=  2.6800E-17
Convergence rate is cleanly approaching 16

Modified mesh by introducing a %(dx) random perturbation to each node.
                           5%                5%       0.1%
   N=           7  err=  2.2442E-05 ratio=  7.6263
   N=          15  err=  2.9427E-06 ratio= 10.2754   16.0980
   N=          31  err=  2.8638E-07 ratio=  8.3182   14.3410
   N=          61  err=  3.4429E-08 ratio=  7.1949   13.7633
   N=         121  err=  4.7852E-09 ratio=  7.5066   14.7297
   N=         241  err=  6.3747E-10 ratio=  8.1147   12.7187
   N=         481  err=  7.8557E-11 ratio=  7.1617   10.4981
   N=         961  err=  1.0969E-11 ratio=  7.9580    8.0792
   N=        1921  err=  1.3783E-12 ratio=  8.0216    8.1620
   N=        3841  err=  1.7182E-13

Why Fortran?  Supports colon notation and quad-precision.