Thank you! I failed to see that I used the FE_DGPMonomial<dim> instead of FE_DGQ<dim>. With the latter it makes as you said acutally no difference.
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? -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? I couldn´t figure out the purpose of the disontinuous legendre-polynomials by having a look at the documentation. -Simon Am Mo., 24. Mai 2021 um 17:54 Uhr schrieb Wolfgang Bangerth < [email protected]>: > 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. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/e91a3cb7-d193-b5e4-850f-900ca6a5dea3%40colostate.edu > . > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CAM50jEt2KaUEPkA78k4mfCY8xv%3Dzs_SZs8bh19o4b5G9VkXFmQ%40mail.gmail.com.
