Questions regarding FE spaces and DG

NGSolve
1

Hello,

I hope this message finds you well. I had two questions regarding the Discontinuous Galerkin method and FE spaces which are as follows.

  1. how are the surface integrals over the interior mesh facets calculated in L2 space as we do not have any nodes on the mesh element facets?

  2. In the H1 space, the nodes are on the vertices/edges of the mesh elements. As these degrees of freedoms are shared between different adjacent elements, I was wondering if we actually can use Discontinuous Galerkin method in the H1 space even with dgjumps=True? In other words, does H1 space allow discontinuity between elements?

Thank you,
Arshia

2

Hi Arshia,

regarding 2: You can break up the continuity of the H1 space like this

fes = Discontinuous(H1(mesh, order=2))

Then every element gets it’s own copy of previously coupled dofs and basis functions become element-wise local.

Best wishes,
Henry