On a discrete scheme for the Mullins-Sekerka flow and its fine properties

02/27/2022

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by   Tokuhiro Eto, et al.

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The Mullins-Sekerka problem is numerically solved in ℝ^2 with the aid of the charge simulation method. This is an expansion of a numerical scheme by which Sakakibara and Yazaki computed the Hele-Shaw flow. We investigate a sufficient condition for the number of collocation points to ensure that the length of generated approximate polygonal curves exactly decrease step by step. Moreover, changing fundamental solutions of the charge simulation method, we are successful to establish a numerical scheme which can be used to treat the Mullins-Sekerka problem with the right contact angle condition.