Nonlinear Parabolic Free Boundary Problems
The 14th open problem cited in the Proceedings of the Workshop on `Free Boundary Problems', held in Freie Univ., Berlin (1977, Vol.I, page 185) is related to the optimal error estimates for the finite element approximations to a single phase nonlinear Stefan problem in one space dimension, and under this programme we have successfully derived these a priori error estimates, (cf. -, - in the list of publications (with P.C. Das)).
Subsequently with one of my Ph.D. students Dr. Jones, we have worked on superconvergence results and qualocation methods for parabolic free boundary problems (cf. ,  in the list of publications and Thesis of Dr. Jones).
To expand the scope of the present method, I have jointly worked with R.S. Anderssen from CMA, ANU (Canberra) on a free boundary problem arising in polymer technology (ref. in the list of publications ).