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[Martin Sandve Alnæs <785874@xxxxxxxxxxxxxxxxxx>]

Using cpp.solve with "cg" and "default" instead of
VariationalProblem.solve fixes the NaN problem. The numbers are still
way off though:

Correct value is 3.14
CG 1 0 3.14000030019 165.429684591
CG 1 1 3.14000030019 165.429684591
CG 1 2 3.14000021752 165.429687084
CG 1 auto 3.12655064226 165.420523845
DG 2 0 2.34727023515e-10 290.790009255
DG 2 1 2.34727023515e-10 290.790009255
DG 2 2 3.92499865818 399.67114339
DG 2 auto 2.61666666667 565.213492026
DG 1 0 -3.8036831125e-08 399.652641011
DG 1 1 -3.8036831125e-08 399.652641011
DG 1 2 3.14 399.669087621
DG 1 auto -4.37743013134e-15 399.65264101

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https://bugs.launchpad.net/bugs/785874

Title:
  Projection of x is not accurate

Status in DOLFIN:
  New

Bug description:
  I've tested that projecting x works without the scaling bug that was
  just fixed, using dimensions 1,2,3 and both DG and CG from 0 to 3
  degrees. I print the max and min values of the vector of the
  projection function, and the values are _close_ to 0 and 1 but not to
  machine precision. The script is below.

  There's up to 2.7% error in the 3D case. Is the projection form
  integrated accurately enough? All but the DG0 function space should be
  capable of representing x exactly. Not sure if this is a dolfin or ffc
  bug.

  
  from dolfin import *

  def mcx(dim):
      if dim == 1:
          mesh = UnitInterval(20)
          cell = interval
          x = cell.x
      if dim == 2:
          mesh = UnitSquare(20, 20)
          cell = triangle
          x = cell.x[0]
      if dim == 3:
          mesh = UnitCube(20, 20, 20)
          cell = tetrahedron
          x = cell.x[0]
      return mesh, cell, x

  for dim in range(1, 4):
      mesh, cell, x = mcx(dim)
      minval, maxval = 1.0, 0.0
      #print dim, "DG"
      for degree in range(3):
          V = FunctionSpace(mesh, "DG", degree)
          u = project(x, V)
          #print dim, degree, u.vector().min(), u.vector().max()
          minval = min(minval, u.vector().min())
          maxval = max(maxval, u.vector().max())
      #print dim, "CG"
      for degree in range(1, 4):
          V = FunctionSpace(mesh, "CG", degree)
          u = project(x, V)
          #print dim, degree, u.vector().min(), u.vector().max()
          minval = min(minval, u.vector().min())
          maxval = max(maxval, u.vector().max())
      print minval, maxval