[petsc-users] FE discretization in DMPlex

[Matthew Knepley]

On Fri, Sep 5, 2014 at 10:55 PM, Justin Chang <jychang48 at gmail.com> wrote:

> Hi all,
>
> So I understand how the FEM code works in the DMPlex examples (ex12 and
> 62). Pardon me if this is a silly question.
>
> 1) If I wanted to solve either the poisson or stokes using the
> discontinuous Galerkin method, is there a way to do this with the built-in
> DMPlex/FEM functions? Basically each cell/element has its own set of
> degrees of freedom, and jump/average operations would be needed to
> "connect" the dofs across element interfaces.
>
> 2) Or how about using something like Raviart-Thomas spaces (we'll say
> lowest order for simplicity). Where the velocity dofs are not nodal
> quantities, instead they are denoted by edge fluxes (or face fluxes for
> tetrahedrals). Pressure would be piecewise constant.
>
> Intuitively these should be doable if I were to write my own
> DMPlex/PetscSection code, but I was wondering if the above two
> discretizations are achievable in the way ex12 and ex62 are.
>

Lets do RT first since its easier. The primal space is

  P_K = Poly_{q--1}(K) + x Poly_{q-1}(K)

so at lowest order its just Poly_1. The dual space is moments of the normal
component
of velocity on the edges. So you would write a dual space where the
functionals integrated
the normal component. This is the tricky part:

  http://www.math.chalmers.se/~logg/pub/papers/KirbyLoggEtAl2010a.pdf

DG is just a generalization of this kind of thing where you need to a) have
some geometric
quantities available to the pointwise functions (like h), and also some
field quantities (like
the jump and average).

I understand exactly how I want to do the RT, BDM, BDMF, and NED elements,
and those
will be in soon. I think DG is fairly messy and am not completely sure what
I want here.

   Matt


> Thanks,
> Justin
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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