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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