Adaptive solution of parabolic free boundary problems with error control

International Meeting on Free Boundary Problems, Theory and Applications, Crete, June 1997, Pitman.

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

Alfred Schmidt
Institut fur Angewandte Mathematik
Universitat Freiburg
7800 Freiburg, Germany

Claudio Verdi
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy


We derive a posteriori error estimates in natural energy norms with weights. They are useful in localizing the error extraction in regions of interest, and form the basis of an adaptive procedure. We use them to study the evolution of a persistent corner singularity and elucidate the issue of critical angle for instantaneous smoothing.