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.
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Wolfgang Bangerth email: [email protected]
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