# Finite Element Solution to Poisson Equation with Boundary Condition at Infinity

I am solving the simple poisson equation $$-\nabla \cdot (\epsilon\nabla u) = \rho$$ using a finite element mesh (rho is just a point charge). I would like to implement a boundary condition such that $$\lim_{r \to \infty} u(r) = 0$$ Is it possible to implement this boundary condition? I.e. Can I place a boundary condition on the boundary of the mesh that will simulate the above limit?

Thanks

• You could use a mesh which is "large enough" to simulate $r \rightarrow \infty$ and set $u = 0$ on its border... or did I miss something in your question ? – lmsteffan Sep 5 '14 at 17:06
• Thanks for the comment. Yes, this is what I am currently doing at the moment. I was just wondering if there was a "cheaper" solution computationally, as I have to quadruple my mesh size to get good results, and I am only interested in a small region around the source charge. – DJames Sep 5 '14 at 17:10
• What basis functions are you using? – user14717 Sep 5 '14 at 18:00
• Linear Lagrange basis functions. – DJames Sep 5 '14 at 18:50