dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

What we have implemented for DG is the ability to define integrals
over interior facets that have contributions from both sides of the
facet, so you can write

    v('+')*v('-')*avg(v)*jump(u, n)...

It's a little different from what you have in that the integral is
over all interior facets in the mesh, not just along some given
surface.

Perhaps you could extract all the cells in the mesh that border to the
common surface, so instead of having some interior surface, you have
an interior mesh that contains the surface and each interior facet in
that mesh connects to exactly two cells, one on each side.

/Anders


On Thu, Jan 18, 2007 at 09:24:01AM +0100, Johan Hoffman wrote:
> Garth and Anders,
> 
> I am interested in solving a problem where I a priori specifies an inner
> surface (aligned with cell faces) where the solution is discontinuous. The
> coupling of the solution over the discontinuity is taken cared of by a
> surface integral over that inner surface (like a penalty term).
> 
> For this I expect to need:
> 
> (1) a data structure with "double nodes" at a predefined surface (=
> collection of nodes/faces).
> 
> (2) for the nodes on the surface; the ability to assemble only
> contribution from either side of the surface for the "double nodes"
> respectively (where the two sides of the surface may be represented by a
> MeshFunction for example).
> 
> (3) a surface integral defined over an inner surface.
> 
> I suspect that some parts of (1)-(3) is already in place, as part of the
> DG work? What remains to be done to handle this problem?
> 
> /Johan
> 
> 
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