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Zeitschrift für Analysis und ihre Anwendungen


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Volume 8, Issue 1, 1989, pp. 57–68
DOI: 10.4171/ZAA/336

Published online: 1989-02-28

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

Uwe Streit[1]

(1) Technische Universität Chemnitz-Zwickau, Germany

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 $$u \in W_2^{1,1} (\Omega_T) \cap L_{infty} (0, T; W_2^1 (\Omega)) \:\: \mathrm {and} \: s \in W_4^1 (0, T)$$ 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.

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Streit Uwe: Error Estimates for the Explicit Finite Difference Method Solving the Stefan Problem. Z. Anal. Anwend. 8 (1989), 57-68. doi: 10.4171/ZAA/336