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I know the weak form of the Poisson problem

[itex]\nabla^2 \phi = -f[/itex]

looks like

[itex]\int \nabla \phi \cdot \nabla v = \int f v[/itex]

for all suitable [itex]v[/itex]. Is there a similarly well-known form for the slightly more complicated poisson problem?

[itex]\nabla (\psi \nabla \phi ) = -f[/itex]

I am writing some finite element code and variational/weak forms are very handy.

Thanks in advance

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# Weak Form of the Poisson Problem

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