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I'm trying to solve an electrowetting problem, by using the finite element Galerkin method. The problem is to find simultaneously the shape of the liquid drop and the distribution of potential in electrode and air.

I've calculated the residuals for the potential u (Ru), in both air (Ru2) and electrode (Ru1) (as seen in the figure inside the attachement) as well as the derivatives with respect to uj (for the jacobian). I also have calculated the free surface (f(θ)) residuals (Rf), and their derivatives with respect to fj. Finally i have calculated the volume constraint residual (Rv) for the liquid drop, and its derivatives with respect to f.

I'm having a problem calculating the derivatives of Ru2 with respect to fj.

Ιn the attachment you can find all the equations i mentioned earlier. And the actual question (in the third page).

Do you have any suggestion on how this can be done ?

Thanks in advance.

HellRaiZer.

P.S. If this is the wrong forum please move it to the correct one.

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# Electrowetting simulation problem

Can you offer guidance or do you also need help?

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