Front Tracking Methods for One-Dimensional Moving Boundary Problems

Abstract

In a series of papers (cf.Section 6) we showed how a combination of the two main attitudes towards MBPs (moving boundary problems), i.e. with or without explicit reference to the moving boundaries, may yield efficient numerical schemes in the case of one space dimension. In fact, classical formulations often suggest a simple front tracking procedure, especially if the equations restricted to the subdomains are linear, while weak formulations, based on nonlinear, possibly degenerate or singular equations in the whole domain (with fixed boundaries), provide a convenient tool for the error analysis. Though there is a large number of numerical methods for MBPs, it should be noted that many of them, especially those of front tracking type, suffer from a lack of rigorous error analysis. There is no place for a review on error estimates here.Instead, we refer to Nochetto & Verdi (1988).