Number of dofs: 33282. What does it mean?

Question

I am solving a static problem on a 2D mesh - Unitsquare.

I specify the number of cells in each direction as (64, 64). Therefore the total number of cells in mesh become nearly 3850. I saw that the number of dof is 33282.

Similarly, when I change the mesh to (4000, 4000), the total number of cells I believe should be nearly 16 million, while the dof I see are 128,032,002 (128 million).

For a (1000,1000) Unitsquare, the total cells should be 1 Million. The no. of dof is 8,008,002.

What are these dofs? Are these dependent on the physics of the problem and the BC's applied? What would be the number of nodes for such a mesh?

Answer 1

Dofs are "degrees of freedom". For a simple scalar problem with a linear Lagrange basis, "CG1" or "P1", the number of dofs will be the same as the number of vertices in the mesh. Using a different basis (e.g. CG2) may have dofs on edges, or cell centered. Vector valued solutions have more dofs at each point.
It looks like you have a vector CG2 function.