# [deal.II] Re: Different time steps lead to different asymptotic values for the residual in a heat equation

```After further tests I noticed:
-> The calculation also has problems if the boundary is equal to the
initial values, i.e. the gradients should be 0 everywhere
-> The time step size is not the reason for the behaviour, the calculation
goes through without any problem if I neglect the gradients (d_tT = 0), but
if I instead just take a look at the gradients (\nabla^2 T = 0), for a
certain level of initial values and boundary values I get the described
behaviour
-> When varying the equation structure from explicit euler to implicit
euler via Crank-Nicholson using theta, I notice:
--> For values of theta below 0.5: My result gets instable and starts
fluctuating
--> For values above theta=0.5: The result is stable, but the residual
never decreases below a certain threshold.```
```
Thus I assume there must be a numerical problem/inaccuracy somewhere, but I
could not find the point yet. Nevertheless, it looks like as if the
gradient functions create larger inaccuracies for large values than the
value-function itself.

What can I do further as debugging for getting more precise results?

Thanks!

Am Dienstag, 10. April 2018 18:30:06 UTC+2 schrieb Maxi Miller:
>
> This question might be related to earlier of my questions, but finally I
> could not find an explanation for the behaviour yet, thus this question.
>
> I intended to calculate the time-dependent heat equation with constant
> factors, using the newton method (such that time-dependent factors can be
> implemented later) and automatic differentiation. Now I added an offset to
> the initial values and the border values, such that both are lifted
> equally. Nevertheless I found out that if I either reduce the time step
> length or increase the offset value, the residual value I am using for
> controlling the solution progress initially decreases fast, but then slows
> down at a certain value depending on the offset value and the time step
> size. Below a certain time step size or above a certain offset value the
> value never gets smaller, and the best calculated step length goes towards
> 0 (compared to close to 1 before).
>
> I do not understand that behaviour. Based on initial tests my code should
> work correct, nevertheless it quits for certain values. What could be the
> reason for that? I attached the code to the question, it should be
> self-contained. Changing of the parameters can either be done using the
> OFFSET-parameter or the time_step parameter in the parameter.prm-file
>
> Thanks!
>

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