# Dynamic order DG basis

This is an implementation of a Discontinous Galerkin (DG) basis that supports (element-wise) varying local finite elements. In particular, one can set the local polynomial degree at runtime. Currently, this is only fully implemented for a Qk basis, but most parts should be interchangeable:

- The
`DynamicDGPreBasis`

is quite universal, one has to modify the`Node`

- The
`DynamicOrderNode`

takes a`Cache`

template parameter. This cache gives local FE which are asked for*by order*. - The
`DynamicOrderLocalFiniteElementCache`

implements such a cache taking another`Factory`

which produces the actual finite element (so if you want different elements, say, e.g., Gauss-Lobatto, you only need to provide a suitable factory and change the template parameter)

If you need a more general `Node`

(e.g. to deal with varying geometries (which are assumed to be uniform in the `DynamicOrderNode`

)), you'd have to implement a node similar to the given one. However, I can't make the Node type a template parameter of the `DynamicDGPreBasis`

(which would be cleaner) as the nodes needs also a `TreePath`

template argument itself which I do not know beforehand. However, aside from the hardcoded `Node`

type (and the form of its constructor), the pre-basis does not make any further Qk-specific assumptions as far as I can see.

I haven't tested this too broadly, yet (before this, I used another implementation which made more assumptions), so comments and tests are highly appreciated. Also, if things can be done better or differently, I'm open for comments.

Cosmetic things I see that maybe should be discussed:

- the whole
`DynamicFooBar`

class naming scheme - code spread through three different header