dolfin team mailing list archive

[Dag Lindbo <dag@xxxxxxxxxx>]

Johan Hake wrote:
> Hello!
>
> I am simulating the diffusion of Calcium ions within an electrical field, 
> i.e., solving the Diffusion Advection (Convection) equation. The field is not 
> solenoidal.
>
> This workes fine for fields with small absolute values. When the typical field 
> get above a certain value, the solution starts to behave peculiarly. It 
> converges but I get negative values of concentration and it becomes very 
> dependent on the mesh size.
>
> My bilinear Diffusion Advection form with homogenous Neumann boundaries look 
> like: (skipping konstants)
>
> ( dot(grad(v),grad(u)) + u*dot(E,grad(v)) )*dx
>
> where v is the test function, u trial function and E the electrical field.
>
> Having basic FEM knowledge, I have heard of the stabilizing method of 
> Petrov-Galerkin, but I have no experience using it. I found some very usefull 
> explainations in Dag Lindbos Master thesis :).

Wow, you found that!

> Do you think this method could be usefull to try out? If so, how should this 
> be formulated in FFC.

Yes, SU/PG is very solid. I believe I cite the original paper if you 
need the details. As I recall, Garth has published papers on this topic.

In any case, there used to be a convection/diffusion module in DOLFIN. 
It contains both the forms and routines needed to compute the 
stabilization. Take a look under src/modules/convdiff/dolfin/ in DOLFIN 
0.6.4. It was probably Garth who wrote this module.

Cheers!
/Dag

> Many thanks in advance!
>
>
> Johan
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