On 5/25/21 1:41 AM, Simon Wiesheier wrote:
However I am wondering why FE_DGPMonomial<dim> gives my quite good results as
well. As I said, for "fine meshes" the results of the local and global
approach are nearly the same and for coarse meshes, i.e. just one or two times
globally refined meshes, the biggest deviation also reaches not more than 5%.
I didn´t have to use FE_DGPMonomial so far. I´ve seen that for degree=1 this
element has only 3 dofs per cell for a scalar problem in 2D, i.e I can not
extrapolate the 4 qp-values to the nodes. But let´s assume I use this element
for my local approach.
-What is the relations of the resulting 3 nodel values to the 4 qp-values? Is
it still something like minimizing the squared difference or is the idea a
different one?
Yes, that's what the *projection* does: It minimizes the difference in some
kind of norm.
-And why is there a difference at all between the local and global approach?
Should the global approach not result in a block-diagonal matrix as well?
The projection is local (=the matrix is block diagonal) if the space is
discontinuous. That is, you should get the same result whether you do the
local or the global projection for both FE_DGQ and FE_DGPMonomial, along with
all other discontinuous elements.
If you get different results between local and global projection for
FE_DGPMonomial, it would be interesting to investigate why.
Best
W.
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Wolfgang Bangerth email: [email protected]
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