# Imposing boundary conditions in a finite element sense

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.

• It's not Neumann as written. What is the PDE? – user7530 Jun 16 '14 at 20:42
• @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 – Ellya Jun 16 '14 at 20:54
• An interesting condition. Consider asking at Computational Science, which has a fair number of finite-elementists. – user147263 Jun 25 '14 at 21:49