Periodic Boundary Condition in General Form PDE -- No Solution for very Simple Equation

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Dear COMSOL community,

I have a lack in understanding solving PDE with PBC, which I can break down to a very simple example, i.e. finding a solution for . The height and width of the 2D simulation domain is , and at the top and bottom a Dirichlet BC () should be applied, while at the left and right site a periodic BC should be applied.

Integrating above equation twice, is given as and from the Dirichlet BC we get and from the periodic BC .

However, when implementing this in the COMSOL general form PDE interface and solving using a Stationary Solver, I do not get the result but an error "Failed to find a solution. The relative error (0.0092) is greater than the relative tolerance.", even not when I use the calculated solution as initial values. However, when replacing the periodic BC at the left and right Interface with a Dirichlet BC , I get the expected result. Therefore, I have two questions:

  • Why don't I get any result when using periodic BC at the left and right interface?
  • Why does the periodic BC not overwrite the default Zero Flux 1 BC, but contribute to it? I also implemented what is suggested here, which then overwrites the Zero Flux 1 BC, but I get the same error as using the implemented Periodic Condition.

Attached is a file of the simulation.

Thank you in advance!



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