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 |
URI: | http://hdl.handle.net/2003/25098 http://dx.doi.org/10.17877/DE290R-15788 |
Issue Date: | 2002 |
Provenance: | Society for Industrial and Applied Mathematics |
URL: | http://link.aip.org/link/?SNA/40/1184/1 |
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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StableTimeDiscretization.pdf | 232.4 kB | Adobe PDF | View/Open |
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