## use DGPk instead of OPB finite elements

### Description

Use `\mathcal{P}^k`

finite elements for discontinuous Galerkin instead of `OPBLocalFiniteElementMap`

.

### Proposal

The reason for using `OPBLocalFiniteElementMap`

in DORiE is just because there is no implementation of `\mathcal{P}^k`

elements for discontinuous Galerkin in pdelab. However, these elmenets are said to be slower because are created with monomials.

Therefore, the idea is to create the implementation of `\mathcal{P}^k`

for dg so that we can use it in DORiE.

The impliementation is easy but lengly. As I did for raviart thomas elements (see !105 (merged)), to create dg elements out of non-dg elements is enough to

- inheriting the desired element,
- overloading the method
`localCoefficients()`

to export`DGLocalCoefficients`

and, - overloading the exported
`Traits`

.

Then, one would have to create a respective pdelab finite element map in order to create grid function spaces out of them.

### How to test the implementation?

Everything works as before (very likely faster in simplices)