Error Estimates for the Explicit Finite Difference Method Solving the Stefan Problem

Abstract

The paper deals with a well-known finite difference method for solving the one-dimensional two-phase Stefan problem. Under assumptions on the data which assure a regularity

of the temperature $u$ and the moving boundary $s{L}_2$-convergence rates $O(h)$ for the approximations of $u$ and $s$ are derived. Additionally, a case of much weaker regularity is considered.