Dear Kyusik, > I'm sorry to tell you that actually I don't know how to project > grad_solution into the vector-valued FE space.... > > Do you happen to know some example tutorial code that includes it....? >
Off the top of my head, no I don't know of an example tutorial that demonstrates it. But you're effectively solving a least-squares problem for the solution gradient so its relatively straight-forward to do: 1. Create a vector-valued finite element system (maybe an FESystem<dim>(FE_Q<dim>(1),dim) ) and use it to distribute DoFs onto a new DoFHandler. 2. Create a mass matrix "M" with the new DoFHandler. 3. Create a RHS vector "f" of the form f_i = \int_\Omega f(x) \phi_i(x) dx . Here f(x) = \grad \psi (x) is the gradient of the solution evaluated at point x and \phi_i is a vector-valued shape function. So you need to obviously compute the gradient of the solution at all quadrature points when doing integration - you would do this with the function I mentioned previously. 4. Solve the linear system M.d = f, where "d" represents the (continuous) gradient of the solution to the scalar problem. There's some useful information in the introduction to the VectorTools namespace <https://www.dealii.org/8.5.0/doxygen/deal.II/namespaceVectorTools.html> (namely on projection and the form of the RHS vector), so you can look there as well for more information. As I said before, you could avoid these complexities by expanding your original equation into the two separate terms. However, the benefit to the projection approach is that you can evaluate this term for one order lower polynomial since you don't need to directly compute second derivatives. With the projection one might incur some loss of accuracy of the gradient field, but I'm not quite sure to what extent this would affect your calculation. Regards, Jean-Paul -- 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. For more options, visit https://groups.google.com/d/optout.
