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Numerical analysis of moving boundary problems using the boundary tracking method

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Abstract

A new numerical scheme of the boundary tracking method for moving boundary problems is proposed. A key point of the scheme is to avoid concentration of tracking points on the moving boundary, and a convergence theorem is proved for the curve shortening problem. Some numerical examples for the curve shortening problem and the Hele-Shaw problem by the proposed scheme are shown.

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  1. Department of Mathematics, Hiroshima University, 739, Higashi-Hiroshima, Japan

    Masato Kimura

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  1. Masato Kimura
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Correspondence to Masato Kimura.

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Kimura, M. Numerical analysis of moving boundary problems using the boundary tracking method. Japan J. Indust. Appl. Math. 14, 373–398 (1997). https://doi.org/10.1007/BF03167390

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  • DOI: https://doi.org/10.1007/BF03167390

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