Adapting meshes and time-steps for phase change problems

Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (9), 8 (1997), 273-292.

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 address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.