[firedrake] Hi everyone,

Justin Chang jychang48 at gmail.com
Wed Jul 15 21:03:21 BST 2015


Lawrence,

It looks to me that the trial functions are enriched on the edge residuals.
I am guessing that's what was meant by the multiscale aka "enrichment"
functions. This other paper written by the same guys offers some
explanation:

http://epubs.siam.org/doi/pdf/10.1137/080724381

My only question is what the Finite Element Spaces would look like within
Firedrake - would it be a concatenation of two separate function spaces (P1
and RT0) or would the basis function look completely different? I could be
wrong, I may need to do a little more research on this first.

Thanks,
Justin

On Wed, Jul 15, 2015 at 5:54 AM, Lawrence Mitchell <
lawrence.mitchell at imperial.ac.uk> wrote:

> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> On 15/07/15 11:46, Justin Chang wrote:
> > I would like to try out the Petrov-Galerkin Enrichment Method
> > (Barrenechea et al 2007) for a mixed-poisson/Darcy equation.Here is
> > the link to the paper:
> >
> > http://www.sciencedirect.com/science/article/pii/S0045782507000059
> >
> > Basically, this method starts with the P1/P0 combination and
> > enriches both velocity and pressure trial functions with
> > multi-scale functions. Is this easily doable within Firedrake?
>
> Can you say a little more?  It looks like I enrich the velocity space
> with RT0 but somehow only locally (such that I can solve a local
> H(div) problem to get a correction?), but I don't really know enough
> about the method to say whether you could do it.
>
> Lawrence
>
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