dolfin team mailing list archive

["Johan Hoffman" <jhoffman@xxxxxxxxxx>]

Great work! Should be interesting to try out.

/Johan

> Discontinuous Galerkin is now supported by FFC and DOLFIN.
>
> A demo is available in src/demo/pde/dg in DOLFIN.
>
> Here's an example for implementation of an interior penalty method
> for Poisson's equation:
>
>   DG1 = FiniteElement("Discontinuous Lagrange", "triangle", 1)
>   DG0 = FiniteElement("Discontinuous vector Lagrange", "triangle", 0)
>
>   v = TestFunction(DG1)
>   u = TrialFunction(DG1)
>   f = Function(DG1)
>   g = Function(DG1)
>   n = Function(DG0) # facet normal
>   alpha = Constant()
>
>   a =  dot(grad(v), grad(u))*dx \
>      - dot(avg(grad(v)), jump(u, n))*dS \
>      - dot(jump(v, n), avg(grad(u)))*dS \
>      - alpha*dot(jump(v, n), jump(u, n))*dS
>
>   L = v*f*dx + v*g*ds
>
> Since this has not yet worked its way into the manual, here's a short
> summary of the new supported operators:
>
>   v('+')     - take value v^+ of v at the '+'-side of a facet
>   v('-')     - take value v^- of v at the '-'-side of a facet
>   avg(v)     - average 0.5*(v^+ + v^-)
>   jump(v, n) - jump with respect to normal, either
>                v^+n^+ + v^-n^- or v^+.n^+ + v^-.n^-
>                depending on whether v is scalar or vector valued
>   dS         - integral over an interior facet
>
> Currently, only 2D is supported (triangular meshes), but 3D is not far
> away.
>
> Thanks to Kristian Oelgaard for a very good job on implementing DG in
> FFC and DOLFIN!
>
> /Anders
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