The initial/Neumann boundary-value enthalpy formulation for the two-phase Stefan problem is regularized by smoothing. Known estimates predict a convergence rate of ε 1 2, and this result is extended in this paper to include the case of a (nonzero) residual in the regularized problem. A modified Newton Kantorovich framework is established, whereby the exact solution of the regularized problem is replaced by one Newton iteration. It is shown that a consistent theory requires measure-theoretic hypotheses on the starting guess and the Newton iterate, otherwise residual decrease is not expected. The circle closes in one spatial dimension, where it is shown that the residual decrease of Newton's method correlates precisely with the ε 1 2 convergence theory.
|Original language||English (US)|
|Number of pages||15|
|Journal||Journal of Approximation Theory|
|State||Published - Sep 1990|
ASJC Scopus subject areas
- Numerical Analysis
- Applied Mathematics