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[Martin Sandve Alnæs <785874@xxxxxxxxxxxxxxxxxx>]

The below script shows some strange behaviour with 'auto' quadrature
degree and DG elements.

The script integrates du/dx over a unit square with u = the projection
of 'pi x' into some space.

For DG spaces of degree 1 and 2 and several choices of quadrature
orders, the result is either completely wrong or NaN.

Am I missing something here or should this be working better?
Also note that for CG elements the result of 'auto' quadrature degree is worse than 0.


from dolfin import *

# Projection which takes form compiler parameters
def myproject(expr, space, params):
    if 1: # Set to 0 to use the regular project and ignore params
        U = Function(space)
        u = TrialFunction(space)
        v = TestFunction(space)
        a = inner(u,v)*dx
        L = inner(expr,v)*dx
        problem = VariationalProblem(a, L, form_compiler_parameters=params)
        problem.solve(U)
    else:
        U = project(expr, space)
    return U

def test(fam, deg, qd):
    ffc_opt = { 'representation': 'quadrature', 'quadrature_degree': qd }
    n = 90
    mesh = UnitSquare(n,n)
    V = FunctionSpace(mesh, fam, deg)
    u = myproject(3.14*triangle.x[0], V, ffc_opt)
    a = u.dx(0)*dx
    dudx = assemble(u.dx(0)*dx, form_compiler_parameters=ffc_opt)
    print fam, deg, qd, dudx, norm(u.vector())

# Summary of the output is embedded in comments below:
print "Correct value is", 3.14
test("CG", 1, 0) # 3.14
test("CG", 1, 1) # 3.14
test("CG", 1, 2) # 3.14
test("CG", 1, 'auto') # 3.12 (worse than qd=0!)

test("DG", 2, 0) # NaN
test("DG", 2, 1) # NaN
test("DG", 2, 2) # NaN
test("DG", 2, 'auto') # 2.61 == 3.14/1.2

test("DG", 1, 0) # NaN
test("DG", 1, 1) # NaN
test("DG", 1, 2) # 3.14
test("DG", 1, 'auto') # almost 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