A new convergence proof for approximations of the Stefan problem

Robert Eymard (1) , Thierry Gallouët (2)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
2 I2M - Institut de Mathématiques de Marseille

We consider the Stefan problem, firstly with regular data and secondly with irregular data. In both cases is given a proof for the convergence of an approximation obtained by regularising the problem. These proofs are based on weak formulations and on compactness results in some Sobolev spaces with negative exponents.

Domaines: Analyse numérique [math.NA]

Robert Eymard, Thierry Gallouët. A new convergence proof for approximations of the Stefan problem. Discrete and Continuous Dynamical Systems - Series A, 2023, 43 (3&4), pp.1383-1399. ⟨10.3934/dcds.2022094⟩. ⟨hal-03693568v2⟩