A posteriori error control of free boundary problems

A posteriori error estimators are computable quantities depending on the discrete solution(s) and the data, which provide upper (and lower) bounds for the error; they are thus instrumental for adaptivity. This paper assesses the derivation of a posteriori error estimators in the context of free boundary problems (FBPs). The discussion is based on simple examples, from contact problems to degenerate parabolic equations and curvature driven flows, and addresses both space and time discretization as well as both energy and maximum norm estimates (including interface error estimates).