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@imperial.ac.uk> wrote:
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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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