Dear Daniel and Wolfgang, Thank you very much! In fact, I only want the gradient of periodic, not the Dirichlet periodic boundary. I thought they are same in periodic boundary conditions before, i.e. all informations of the solution on the face pairs are same. Now, I get that I have made mistake.

Why I need the gradient of periodic only? Because in my case, I have some boundary integrals in my cost functional, I need to make all of them equal to zero, so I can choose the gradient of periodic only. But in the analysis of weak solution of original PDEs in my case, the space of trial and test funcution are (H^1) * (H^1) * (L^2) * (H^1) (sobolev space), as there are the gradient of 1st, 2nd, 4th component in the weak form. And I choose C0 * C0 * C0 * C0 FEM space So I cannot make sure the continuity of the gradient in boundary or internal faces. But I don' know how to implement what I need? Maybe some penalty part like in Discontinuous Gradient Method to make up for continuity of the gradient? Thank you very much! Best, Chucui -- 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.