Authors: Schweizer, Ben
Title: A Stable Time Discretization of the Stefan Problem with Surface Tension
Language (ISO): en
Abstract: We present a time discretization for the single phase Stefan problem with Gibbs--Thomson law. The method resembles an operator splitting scheme with an evolution step for the temperature distribution and a transport step for the dynamics of the free boundary. The evolution step involves only the solution of a linear equation that is posed on the old domain. We prove that the proposed scheme is stable in function spaces of high regularity. In the limit $\Delta t\to 0$ we find strong solutions of the continuous problem. This proves consistency of the scheme, and additionally it yields a new short-time existence result for the continuous problem.
Subject Headings: free boundary problem
time discretization
operator splitting
Issue Date: 2002
Provenance: Society for Industrial and Applied Mathematics
Citation: A Stable Time Discretization of the Stefan Problem with Surface Tension, Ben Schweizer, SIAM J. Numer. Anal. 40, 1184 (2002), DOI:10.1137/S003614290037232X
Appears in Collections:Schweizer, Ben Prof. Dr.

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