On 08/24/2017 09:22 AM, Maxi Miller wrote:
In the first case, there is nothing we need to do: we are using a
continuous finite element, and face terms do not appear in the
bilinear form in this case. The second case usually does not lead to
face terms either if we enforce hanging node constraints strongly
(as in all previous tutorial programs so far whenever we used
continuous finite elements – this enforcement is done by the
ConstraintMatrix
<https://www.dealii.org/8.4.0/doxygen/deal.II/classConstraintMatrix.html>
class together with DoFTools::make_hanging_node_constraints
<https://www.dealii.org/8.4.0/doxygen/deal.II/group__constraints.html#ga3eaa31a679484e80c193e74e8a967dc8>).
In the current program, however, we opt to enforce continuity weakly
at faces between cells of different refinement level, for two
reasons: (i) because we can, and more importantly (ii) because we
would have to thread the automatic differentiation we use to compute
the elements of the Newton matrix from the residual through the
operations of the ConstraintMatrix
<https://www.dealii.org/8.4.0/doxygen/deal.II/classConstraintMatrix.html>
class. This would be possible, but is not trivial, and so we choose
this alternative approach.
Hm. I'm not sure I completely understand the issue any more. The second
part may or may not be correct. I think what it refers to is that not
all variables on a cell are actually degrees of freedom (e.g., if a
variable is defined at a hanging node) but may be tied to other
variables. Taking the derivative with regard to this variable may
therefore not immediately be what one had in mind. It's a different
question whether the result is actually wrong, or whether everything
works out when one distributes the local matrix into the global one with
ConstraintMatrix::distribute_local_to_global(). I think it's entirely
possible that the result turns out to be correct after all.
One would have to think about this some more, I'm afraid.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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