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.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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