AN EASY FINITE ELEMENT IMPLEMENTATION OF THE OBSTACLE PROBLEM FOR POISSON'S EQUATION
Ed Bueler · 2004
where z = 0 is the plane of the wire frame. Now suppose that an obstacle is placed underneath the membrane. Specifically, suppose the obstacle has a continuous and differentiable surface z = ψ(x, y) and that ψ ∣∣ ∂Ω ≤ 0. The problem now becomes to find the region R where u coincides with ψ and to solve −4u = f in the complementary region Ω\R. That is, the problem is to find the minimal energy configuration of the membrane “stretched over” the obstacle. Figure 1 shows an example where Ω is the disc of radius two centered at the origin, the obstacle is the sphere of radius one centered at the origin (in R, that is) and f ≡ 0.