Error norm no change for the Poisson equations with two subdomains

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See for instance:

Manufactured solution method for multi-material

In your code, you are enforcing: D_1\frac{\partial u}{\partial x} = D_2\frac{\partial u}{\partial x} on the interface between the two materials. When D_1\neq D_2, this will cause a discontinuity in the gradient across the interface. To counteract this behavior, you need to do your integration by parts thoroughly, and will end up with a term like this: F += -2*pi*cos(2*pi*0.5)*(D_01*v("-")-D_02*v("+"))*dS(3) where dS(3) is the interface between the two domains. I’ve attached my adaptation o…

for an example with multi material problems with Poisson. Try to first implement a similar approach in your code, and then extend it to 2D when you Get it working.