  Simulations of motion by mean curvature in bounded domains, with applications
to bubble motion and grain growth, rely upon boundary conditions that are only
approximately compatible with the equation of motion. Three closed form
solutions for the problem exist, governing translation, rotation and expansion
of a single interface [1], providing the only benchmarks for algorithm
verification. We derive new identities for the translation solution. Then we
estimate the accuracy of a straightforward algorithm to recover the analytical
solution for different values of the velocity V given along the boundary. As
expected, for large V the error can reach unacceptable levels especially near
the boundary. We discuss factors influencing the accuracy and propose a simple
modification of the algorithm which improves the computational accuracy.
