" When you discretize a function via interpolation of projection, you generally lose most structural properties of the function -- for example, it will have a different mean value, it may lose symmetry if your mesh is not symmetric, it will only be in H^1 even though the original function may have been in C^infty, and vector functions may no longer be divergence free after projection. Some of these issues can be addressed by using specialized operations (e.g., divergence free projections), but you generally have to expect that whatever special property your original function has, the interpolated or projected function will not any longer possess."
So in my case there is no special operation in your mind to make sure f^h at the rotated grid is separated in x and y (e.g., ensuring a certain aspect ratio of the cells,...)? -Math Wolfgang Bangerth <bange...@colostate.edu> schrieb am Fr., 9. Juni 2023, 22:59: > On 6/9/23 12:52, Mathieu wrote: > > > > The fact that f^h is no longer separated changes the solution of my pde > > drastically: > > If I run my program with the analytical f or with f^h on the axis > parallel > > grid, the output is quite similar. This is not so if I run it with f^h > defined > > on the rotated grid. > > And since the axis parallel grid is able to capture the separation, > > I hoped the rotated grid can capture it too. > > But if I understood you correctly, there is no obvious workaround for > this > > issue , right? > > When you discretize a function via interpolation of projection, you > generally > lose most structural properties of the function -- for example, it will > have a > different mean value, it may lose symmetry if your mesh is not symmetric, > it > will only be in H^1 even though the original function may have been in > C^infty, and vector functions may no longer be divergence free after > projection. Some of these issues can be addressed by using specialized > operations (e.g., divergence free projections), but you generally have to > expect that whatever special property your original function has, the > interpolated or projected function will not any longer possess. > > That happens to be one of the many things you just have to live with when > working with discrete functions. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bange...@colostate.edu > 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 dealii+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/f85c0f37-b442-45e7-39de-dab5b86ff121%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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CA%2BwBsdO3Nh8TxfLDhXJWBbY2XLkA8rcCd3jF--SfPtBXX95OhA%40mail.gmail.com.
