An analysis of numerical approximations of metastable solutions of the bistable equation
Donald Estep · Nonlinearity · 1994
We consider finite element methods for the bistable problem that have the same Lyapunov functional as the true solution. We show that the approximations of metastable solutions generated by these methods evolve on the same time scale as the true solution, provided the mesh and time steps are sufficiently fine depending on the initial data and the diffusion constant but not on the length of time of the evolution.