Datapostprocessor first derivative based on what?

[Jaekwang Kim]

Hi, all 

I have asked specific implementation of Datapostprocessor Class a week ago. 

Adding to that.. I suddenly become curious how this class take 'the first derivative' form the solution vector. 

For example, if I solve flow problem with Taylor hood element as step-22 tutorial program, and take the first derivatives of the acquired solution velocity using Datapostprocessor Class, 

I could easily get my target quantities (derivatives) for all same dof points. 

However, I come up with the fact that my finite elements is only C0-continuous...at the vertex where two different elements meet. 

(My taylor element is degree 2 for velocity and degree 1 for pressure. )

If then, on those vertexes, how the Datapostprocessor decides which element to refer for the first, or second derivatives on that dof? 

Thank you

Jaekwang Kim 

[Daniel Arndt]

Jaekwang,

DataOut creates data at each corner of each cell. However, DataOutFilter[1] allows to reduce the number of data to just one value for each vertex.

Answering your question: DataPostprocessor doesn't choose a value but the output includes all of them.

Best,

Daniel

[1] https://www.dealii.org/8.5.0/doxygen/deal.II/classDataOutBase_1_1DataOutFilter.html#aac0c8391641850d7df17352f607123ae

[Wolfgang Bangerth]

> For example, if I solve flow problem with Taylor hood element as step-22
> tutorial program, and take the first derivatives of the acquired solution
> velocity using Datapostprocessor Class,
> I could easily get my target quantities (derivatives) for all same dof points.
>
> However, I come up with the fact that my finite elements is only
> C0-continuous...at the vertex where two different elements meet.

Correct. That means that there are multiple values of the gradient at
vertices, and indeed we put multiple values into the output file.

> (My taylor element is degree 2 for velocity and degree 1 for pressure. )
> If then, on those vertexes, how the Datapostprocessor decides which element to
> refer for the first, or second derivatives on that dof?

It doesn't use locations of DoFs but the vertices of cells. And it outputs the
same vertex as many times as there are adjacent cells, if necessary with
different values. This is the same as if you had, for example, a piecewise
constant field -- every cell is shown in graphical output as a horizontal
plane, and at vertices several of these planes come together.

Best
W.


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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/