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

Uwe Streit

doi:10.4171/zaa/336

JournalszaaVol. 8, No. 1pp. 57–68

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

Uwe Streit
Technische Universität Chemnitz-Zwickau, Germany

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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

u \in W_{2}^{1, 1} (Ω_{T}) \cap L_{in f t y} (0, T; W_{2}^{1} (Ω)) and s \in W_{4}^{1} (0, T)

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.

Cite this article

Uwe Streit, Error Estimates for the Explicit Finite Difference Method Solving the Stefan Problem. Z. Anal. Anwend. 8 (1989), no. 1, pp. 57–68

DOI 10.4171/ZAA/336