Non-unique solution values for FE_Q_DG0

[Jinhyun Choo]

Hello,

While solving a simple problem using FE_Q_DG0 elements, I found that the output data vector (created by DataOut.add_data_vector) has non-unique values for the same point. Attached is an example .pvd file. Here, there are two points of same coordinates (0.1,0.95,0), and the pressure values of the two points are different.

I solved the same problem with FE_Q elements. Then the output file also contains two points of same coordinates (I don't know why), but their solution values are identical.

Could somebody explain why there are two points of same coordinates and why their solution vales are different only in FE_Q_DG0 elements?

Many thanks,

Jinhyun

[Praveen C]

Hello Jinhyun

This is not an error. Since you have discontinuous solution, at a face in 2d you have two different values and at a vertex in 2d you may have 4 different values. When deal.II saves solution files for visualization, it does not do any averaging etc. at face/vertex, hence you will get these different values. In fact solution saved by sampling points cell-by-cell, and points on face/vertex can be repeated in the output file which have same coordinates but different solution value (in case of DG only) because they were evaluated on different cells. I think this gives a true representation of DG solution.

Also see

https://github.com/dealii/dealii/wiki/Frequently-Asked-Questions#the-graphical-output-files-dont-make-sense-to-me----they-seem-to-have-too-many-degrees-of-freedom

Best

praveen

[Jinhyun Choo]

Hi Praveen,

Thank you for your prompt answer. It all makes sense, and now I understand why. Thanks so much!

Best,

Jinhyun