Quasi-optimal error estimates for the mean curvature flow with a forcing term (Q1343177)

A singular perturbed reaction-diffusion equation with a small parameter \(\varepsilon> 0\) is considered. The authors prove a quasi-optimal estimate of order \(O(\varepsilon^ 2|\log \varepsilon|^ 2)\) for the Hausdorff distance between the flow and the approximate interface. The order of the interface error estimate is a consequence of a comparison principle and the explicit construction of suitable sub- and supersolutions.