numerical flux HDG+

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1

Hi,

I am trying to implement an HDG+ method. I am having trouble with a term involving the L^2projection of an unknown.

For example, for an element K [tex]u_h \in \mathcal P_{p+1}(K),\quad\mu\in \Pi_{F\in \partial K}\mathcal P_p(F)[/tex]. I would like to compute

[tex]\int_{\partial K} P_{M} uh \mu ds[/tex]

where P_M is the L^2 projection onto the space [tex]\mathcal P_{p+1}(K)[/tex].

Is possible to implement L^2 projection as operators?

I would appreciate any help.

Thanks.

2

Hi Manuel,

To realize the projected jumps, you simply add the flag “highest_order_dc=True” in your facet fe space, and keep the poly degree the same for both volume and facet fespace.
E.g.:
V = L2(mesh, order=4)
M = L2(mesh, order=4, highest_order_dc=True)

The global linear system with such M consists of cubic polynomials on the facet.

Take a look at section 2.2 of this reference.

Best,
Guosheng

3

Hey Guosheng,

Thanks for your reply. I will check it out and try it.

Best,