A posteriori error control of FBPs

International Meeting on Free Boundary Problems, Theory and Applications, Trento (Italy), June 2002.

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA



A posteriori error estimators are computable quantities depending on the discrete solution(s) and 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).