Open AccessConvergence of a higher order finite difference scheme for two-phase Stefan problems.
Author(s) -
R Martı́nez-Rosado,
F. Castillo-Aranguren,
Rubén Darío Santiago Acosta,
Ernesto M. Hernández-Cooper,
J A Otero-Hernández
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1936/1/012007
Subject(s) - discretization , convergence (economics) , mathematics , scheme (mathematics) , mathematical proof , finite difference , stefan problem , finite difference scheme , order (exchange) , set (abstract data type) , space (punctuation) , work (physics) , finite difference method , grid , mathematical analysis , computer science , geometry , economics , economic growth , operating system , mechanical engineering , finance , engineering , programming language , boundary (topology)
This work establishes a sufficient condition for convergence of a semi-implicit finite difference scheme with variable space grid of fourth order of accuracy in space, previously set by the authors. The scheme is intended to solve one-dimensional two-phase Stefan problems. The proofs of the above-mentioned results are based on estimates which are obtained and subsequently employed in order to find an upper bound of the discretization error both at phases and the interface. The computational behavior of the scheme under the sufficient condition is corroborated by a series of numerical tests.