Dear all, I am projecting gradients of my displacement solution, for instance stresses, which are only available to me at the quadrature points, to the nodes in order to get fields. (However I project many more variables, so I transformed my problem in projecting many scalar variables, but anyway this is not important regarding my question).
-I am doing the projection once by solving a global minimization problem, i.e. minimizing the integral over the whole domain of the squared difference diff = "values at qps - values at nodes". This leads to the typical mass matrix (phi_i, phi_j) which is also provided in the VectorTools namespace. I solve this min.-problem once with a continuous FE_Q und once with a discontinuous FE_DGQ, i.e. I call the very same function body, I just give different DoFHandlers as input. -A second approach for the same discontinuous FE_DGQ is intruduced in step-18 (extensions) by using compute_projection_from_quadrature_points_matrix(), i.e. a local method. (My poly_degree is constructed in a way that I have always as many dofs_per_cell as qps.) My question is if the output, i.e. the nodal values, of both discontinuous approaches (1. given a FE_DGQ to the global min.-problem vs. 2. the local compute_projection_from_quadrature_points_matrix() approach) should be the same, except of numerical errors? 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? Thanks for the input! Best Simon -- 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/f04edf1d-cc06-4732-bb3d-d3e74162ed98n%40googlegroups.com.
