Dear all, I am reading the page : https://www.dealii.org/current/doxygen/deal.II/classFiniteElement.html. I feel confused by the numbering of the degrees of freedom. For example:

FESystem<dim> <https://www.dealii.org/current/doxygen/deal.II/classFESystem.html> fe_basis(FE_Q<dim> <https://www.dealii.org/current/doxygen/deal.II/classFE__Q.html>(2), dim, FE_Q<dim> <https://www.dealii.org/current/doxygen/deal.II/classFE__Q.html> (1),1); As mentioned in Glossary: Describing "degrees of freedom" in this context requires us to simply *enumerate* the basis functions of the space *V**h*. For *Q*1 elements this means simply enumerating the vertices of the mesh in some way, but for higher elements one also has to enumerate the shape functions that are associated with edges, faces, or cell interiors of the mesh. We have a vector u which has 2 components defined on 9 nodes. On each node, there are 2 base functions, so the degrees of freedom are 9*2*2 = 36. And we have a scalar p which has 1 component defined on 4 nodes. On each node, there is one base function, so the degrees of freedom are 4*1*1=4. The total degrees of freedom should be 36+4=40. In the webpage, it gives 2*9+4*1=22 degrees of freedom, it equals the base function with the vector components. [image: image.png] u(0) should have two base element [phi(0),0] and [phi(0) 0], u(1) should have two base elements as well [0 phi(0)] [0 phi(1)], so here should be 4 rather than 2 degrees of freedom. Best regards, -- Yuesu Jin, Ph.D student, University of Houston, College of Natural Sciences and Mathematics, Department of Earth and Atmospheric Sciences, Houston, Texas 77204-5008 346-404-2062 -- 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%2B25a%3DJSXMHpWcN1EC_Nrd28%3DAMGRU5Fd-heZLbJFZqbsrq4MA%40mail.gmail.com.