On 5/22/21 1:22 AM, Simon wrote:
I am aware that I solve a linear system in the first case whereas in the
second case not, but my idea was the following: The first approach minimizes
the squared difference, but if I have as many dofs_per_cell as qps then of
course the squared difference can be minimized to zero for each qp, i.e. the
qp values can directly be transferred to the nodes. And if my understanding is
correct, this is exactly what the second approach does. So in the first
approach I do not do it "directly" but due to its definition and the number of
dofs it should do the same as second.
Of course I compared this approaches in my program. However depending on the
mesh size there are deviations up to percent, with finer meshes this
difference reduces.
Can this deviation be argumented away with the standard argument "this is the
numerics..." or is there is a mathematical difference and both approaches do
something different?
For discontinuous elements, the mass matrix you compute is block diagonal and
the projection can be computed cell-by-cell -- so it shouldn't make a
difference whether you solve the global problem or do it one cell at a time.
If you get different results, it would be useful to investigate how exactly
they are different.
For continuous elements, the projection is not exact in general, and whatever
you compute locally on one cell has to be reconciled with what you compute on
neighboring cells. The global project is one way to do this reconciliation.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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