Improve degree estimation by considering tensor component degrees are not equal

[Martin Sandve Alnæs]

Illustrated by this snippet from Jan Blechta:

from dolfin import *
from ufl.algorithms import estimate_total_polynomial_degree as est

mesh = UnitSquareMesh(42, 42)
P2 = FunctionSpace(mesh, 'CG', 2)
P1 = FunctionSpace(mesh, 'CG', 1)
V = P2*P1

u = Function(V)
print est(u[1]) # 2
print est(split(u)[1]) # 2
print est(u.split()[1]) # 1 - this is only correct

u0, u1 = TrialFunctions(V)
print est(u1) # 2

u0, u1 = TestFunctions(V)
print est(u1) # 2

This is a long standing issue, here's the text from launchpad:

The degree estimation algorithm can be improved by looking at the degrees of components of functions instead of the max degrees.

See fixmes in and calls to degree() in estimate_degrees.py.

The improved algorithm is probably easier to implement with some utilities from the uflacs project, holding until that is considered.

[Martin Sandve Alnæs]

On hold pending integration of some utilities from uflacs which may make this easier to implement correctly.

[Martin Sandve Alnæs]

Note to future implementer of this enhancement: In addition to varying degrees between components of mixed functions, functions in product elements will have varying degrees depending of the direction you take the derivative in.