Yes, thank you for the warning, that could be an issue indeed. In my case I
am using P2 elements, I'll check the best way to approach this, thank you!
Il giorno venerdì 4 aprile 2025 alle 18:29:26 UTC+2 Wolfgang Bangerth ha
scritto:
> On 4/4/25 10:25, Sclah wrote:
> > **
> >
> > Yes! Thank you very much, I was indeed missing the mathematical
> derivation.
> > I better checked my computations and I actually need:
> > /div([I + grad(u)]^{-T})/ instead of /div([I + grad(u)]^{-1})/ but
> following
> > your steps that leads to a similar result:
> > /div([I + grad(u)]^{-T}) = - Finv [grad(grad(u)^T)] Finv/
> > Then I guess that using get_function_hessians() on /u/ is what I need to
> > assemble correctly my weak form.
>
> Yes. I imagine you're aware of that, but if you're using the usual set of
> finite elements, the gradient is discontinuous and so the second
> derivatives
> are not defined at cell interfaces; in general, the second derivative of
> the
> finite element solution is a poor approximation of the second derivative
> of
> the exact solution. (In the extreme case, if you were using linear
> elements on
> triangles, then the gradient is constant and the second derivative is
> always
> zero.)
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>
>
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