On sentinel method of one-phase Stefan problem
Keywords:Sentinel method, Approximate controllability, Stefan’s problem
This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated.
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Copyright (c) 2023 Merabti Nesrine Lamya, Iqbal M. Batiha, Imad Rezzoug, Adel Ouannas, Taki-Eddine Ouassaeif
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