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Say we have a PDE which is well posed with the boundary condition $|\nabla u|=r$ ($r$ constant) on $\partial\Omega$, where $\Omega\subset \Bbb R^n$ is uniformly convex.

How would one impose this condition into a finite element algorithm, does it count as a neumann boundary condition? or must we always have a normal derivative.

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  • $\begingroup$ It's not Neumann as written. What is the PDE? $\endgroup$ – user7530 Jun 16 '14 at 20:42
  • $\begingroup$ @user7530 It is the monge ampere equation $det(D^2u)=f(x,u,\nabla u)$, the boundary condition is called the "second boundary condition" and it arises in optimal mass transport $\endgroup$ – Ellya Jun 16 '14 at 20:54
  • $\begingroup$ An interesting condition. Consider asking at Computational Science, which has a fair number of finite-elementists. $\endgroup$ – user147263 Jun 25 '14 at 21:49

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