[dune-pdelab] Inquiry

[Jö Fahlke]

Am Tue, 20. Sep 2011, 08:44:57 +0200 schrieb Jared Okiro:
> I am a new dune user, and is developing a DG code for a reaction-diffusion
> system.
> When I look at the example code in
> dune/pdelab/localoperator/convectiondiffusiondg.hh,
> I see two ways of doing the residual assembly i.e alpha volume and jacobian
> volume.
> Can someone help me understand the difference between these two functions in
> setting up
> the system?. I am asking this because in standard Galerkin methods, I only
> see alpha volume
> but not jacobian volume also.

Well, jacobian_volume() is needed when you need to assemble and solve a
matrix, i.e. for stationary or implicit instationary problems.  If you don't
want to implement both of alpha_volume() and jacobian_volume() you can derive
your local operator from NumericalJacobianVolume.  This implements
jacobian_volume() using alpha_volume() an numerical differenciation.
Alternatively, if you have a *linear* problem and don't want to implement
alpha_volume(), you can derive your local operator from
JacobianBasedAlphaVolume.

> Finally, my problem is of the form:
> 
> *\frac{\partial u}{\partial t} = D \ Delta u + f(u) = 0  in \Omega,* where
> f(u) is a non-linear function.
> 
> Do I need to do jacobian volume of the temporal operator also or the alpha
> volume is sufficient?

That depends on your time-stepping scheme.

Bye,
Jö.

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