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Periodic boundary conditions involving derivatives of the solution

+2 votes

I am looking to impose a boundary condition of the following form

$$\left.u(x,y)\right|_{\Gamma_{1}} = c \left. \frac{\partial u(x,y)}{\partial x}\right|_{\Gamma_{2}} $$

for a two-dimensional PDE. $\Gamma_{1}$ and $\Gamma_{2}$ are two different parts of the boundary between which a bijective mapping exist. The FEniCS command that does something similar, but without derivatives of the solution, is called PeriodicBC (see description in the FEniCS documentation here 1), but this only works when only $u$, and not its derivatives are involved. Is there a way to make this work also with derivatives?

Many thanks.

asked Nov 29, 2014 by wilhelmbraun FEniCS User (2,070 points)
edited Nov 29, 2014 by wilhelmbraun
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