Hi Wolfgang
Makes complete sense. Do you know of any literature comparing the two
approaches?
Regards
Andrew
>
> Andrew,
>
>> If one were to adopt an adaptive strategy for Step 23 would it not suffice
>> to simply transfer the solution vector X at the end of step n-1 to the
>> refined mesh at the beginning of step n. Thus, you have X_{n-1} (the
>> solution from the old mesh) interpolated to the new mesh at t_n and you use
>> the same interpolation functions defined for the current time step?
>>
>> Is this not essentially the methodology adopted in Step 33? There
>
> And step 31/32, for example.
>
>
>> adaptivity is used but no mention is made of constructing interpolation
>> functions on different meshes.
>
> The point I wanted to make is this: if you discretize first in time , you get
> for the solution at time step n something of the following form (still in
> strong form, not discretized in space):
>
> SomeOperator u^n = u^{n-1} + sources etc
>
> If you now discretize this in space, you get a weak form for u^n_h that's
> something like this:
>
> a(phi^n_i, u^n) = (u^{n-1}_h, phi^n_i) + ...
>
> That means, you have terms in the right hand side where you have to integrate
> shape functions from the previous time step (in u^{n-1}_h) against shape
> functions from the current time step. How to do this is what step-28 shows.
>
> So this is what you need to do if you want to do it right. If you want to
> have
> it easy, you'll transfer your solution to the current time step using the
> SolutionTransfer class, which is an interpolation operation. The right hand
> side then becomes
> (I^n_h u^{n-1}_h, phi^n_i) + ...
> which is a lot simpler to integrate because now all shape functions come from
> the same mesh. Of course, it's not quite the same thing any more.
>
> Best
> W.
>
>
> -------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.tamu.edu/~bangerth/
>
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