Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter

An asymptotic analysis is developed, which guarantees that the equation εa(x)∂uε/∂t = ε divx(a(x)▽xuε) - ψ(uε)/2εa(x) in Rn × (0, T), approximates a flow by mean curvature with an error of order O(ε2). The dependence on space of the relaxation parameter εa(x) is crucial for the stability and accuracy of the finite element approximations based on a local mesh refinement strategy. Several numerical experiments simulate the mean curvature motion of various surfaces and confirm the reliability of the asymptotic analysis.