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[Martin Sandve Alnæs <785874@xxxxxxxxxxxxxxxxxx>]

I've added form_compiler_parameters to project so I can set the
quadrature degree (passed on to the two assemble calls).

This code, using "lu", still shows some problems:

def test2(qd):
    ffc_opt = { 'representation': 'quadrature', 'quadrature_degree': qd }
    mesh = UnitSquare(50, 50)
    V = FunctionSpace(mesh, "DG", 1)
    u = project(triangle.x[0], V, solver_type="lu", form_compiler_parameters=ffc_opt)
    a = u.dx(0)*dx
    M = assemble(u.dx(0)*dx, form_compiler_parameters=ffc_opt)
    uv = u.vector()[:]
    print uv.min(), uv.max(), M

test2(1)
test2(2)
test2(3)
test2('auto')


Output:

nan nan nan
-1.11173074327e-17 1.0 1.0
-9.52912065661e-18 1.0 1.0
0.00666666666667 0.993333333333 8.77744057992e-16

with qd = 2, 3, it looks good, with 1 or 'auto' we have nan or zero.

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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