Bhanu,
In my application, the FESystem is 'fe(FE_Q<dim>(degree+1), dim,
FE_Q<dim>(degree), 1, FE_Q<dim>(degree), dim)'. As you can see there are
three unknown solution variables(lets call them U, p and W), in which
the first and last are vector valued with 'dim' components and the first
one is one degree higher than the last. The boundary
condition/constraint I have is 'W = U' in every component at a
particular boundary with boundary_id. (U dof is present at every W dof
as U is one degree higher than W, but not the other way).
This is not actually true, and it's going to make the algorithm you are
seeking substantially more complicated. Think about a Q3 element for U
and a Q2 element for W: U has nodes at 1/3 and 2/3 along each edge, but
W has nodes only at the midpoint of each edge.
So the algorithm you're seeking cannot be as simple as set some degrees
of freedom equal to others, and the rest to zero. Rather, the problem
you want to solve is in essence what one does in hp finite element
methods where you have a Q3 and a Q2 element coming together at one
edge. You may want to read the paper I wrote with Oliver Kayser-Herold
many years ago about this.
An alternative could be to use FE_Q_Hierarchical instead. That one,
truly, satisfies the property you describe and would make construction
of these constraints easier.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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