# Obstacle Problem

We consider the setting where there is an obstacle lying above the graph in the coupled system (coupled system) . To do this we reformulate our original motion by mean curvature problem into a variational inequality

which can also be considered as the minimisation of

where K is a convex set constraining the graph to lie below the obstacle.To solve this we interpolate the initial curve with cubic splines and then use a relaxtion algorithm to minimise at each time step.

Considering only a constant forcing term in the upward normal direction, that is , Running this with 400 time steps and nodal width , . We see that the curve reaches an equilibrium where the downward forcing of the obstance and mean curvature is enough to overcome to upward forcing on the curve.