I'm solving a 3-d vector Maxwell's wave equation problem with nodal basis
functions. To overcome spurious solution and singularity, the "regularized
Maxwell equation
<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F233149933_Regularized_Maxwell_Equations_and_Nodal_Finite_Elements_for_Electromagnetic_Field_Computations%3FenrichId%3Drgreq-f9f1ce993e048a2fa4a19555b0bfd719-XXX%26enrichSource%3DY292ZXJQYWdlOzIzMzE0OTkzMztBUzoxMDIzMTM5NzY5MjYyMDhAMTQwMTQwNDk2MTE0MQ%253D%253D%26el%3D1_x_3%26_esc%3DpublicationCoverPdf&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7C2ec5fd5b09f04d1949f508dae1cf4792%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638070577855923173%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=S%2BCRm%2FERX40V4gn0M63l7oLsnBV7BSg%2F2gsWD1zTsno%3D&reserved=0>" is applied. The question is, I cannot judge if my solution is same as the one solved with Nedelec elements (shown in the figure, FE_Q(3) on the left with "Nonlinear subdivision Level" and Nedelec(0) on the right) from visualization. Even if the results are identical, FE_Q has dof on nodes and FE_Nedelec has dof on edge, so FE_Q's visualization results always have a asymptotic effect around singularity on the central edge. Is there a away to display nodal-based result as edge-based? FETools::interpolate does not support this because Nedelec is non-primitive.
I think it took all of us a month to get back to your question because it's
not quite clear what it is you want to do. If I understand correctly, you want
to *compare* the two solutions somehow, and for that you tried (i) to
interpolate the Nedelec solution to the FE_Q space and (ii) to interpolate the
FE_Q solution onto the Nedelec space.
The first of these does not immediately work because the Nedelec solution is,
in general, discontinuous at nodes and so the interpolation operator is not
easily defined. The second of these does not immediately work because
FETools::interpolate() does not work for Nedelec target elements.
But in the end, what that points out is that it isn't quite clear to me what
you are trying to do. The two solutions live in different function spaces that
are not nested, and so interpolation in either direction can not preserve the
solution: Even if FETools::interpolate() would work, the FE_Q solution would
not be equal to the interpolated function.
As a consequence, I don't quite know what you would learn from comparing the
interpolated FE_Q solution and the Nedelec solution. My suggestion would be to
treat both the FE_Q solution and the Nedelec solution as L2 functions (namely,
piecewise polynomials, possibly discontinuous). Then compare them as such. In
fact, that would be easy enough if you just output both in a graphical format
via DataOut and show both solutions at the same time; typical visualization
programs also allow you to define derived variables that can, for example, be
the difference between the two solutions which will help you understand how
the two differ.
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/670e45eb-04f9-e41c-3417-ed66e8aaa55a%40colostate.edu.
