libadjoint team mailing list archive

["Marie E. Rognes" <meg@xxxxxxxxx>]

On 06/12/2012 06:06 PM, Patrick Farrell wrote:
> On 11/06/12 11:05, Marie E. Rognes wrote:
> > However, one comment: do we really have any underlying continuous
> > representation of, say, 'u' over the time interval (0, T)? As far as
> > I understand, what we've got is a set/sequence of {u_k} and a set of
> > times {t_i}. Any integration will be some form of guess of what these
> > u_k corresponds to, right? I guess what I'm asking is how you can
> > deduce an integral from a sequence of fields which are decoupled from
> > the original (time-dependent) pde.
>
> That's where you need some notion of what basis function is used in
> space. If you have the values of the function at certain times, and
> want to integrate it, you need to have some expansion of it. So I'm
> not sure that this work is so decoupled from DOLFIN's spacetime work ..

Ok, I see what you mean, and this spurs some possibly interesting ideas...

However, if you know a set of {u_i} and {t_k} and you know that u_i
corresponds to t_k, then at least you could do linear interpolation and
not be too bad off right? However, I think you might need to associate
the time t with the function u_i? Does that make any sense?

--
Marie

--
Marie