Slowly-migrating transition layers for the discrete Allen-Cahn and Cahn-Hilliard equations
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چکیده
منابع مشابه
Slowly-migrating Transition Layers for the Discrete Allen-cahn and Cahn-hilliard Equations
It has recently been proposed that spatially discretized versions of the Allen-Cahn and Cahn-Hilliard equations for modeling phase transitions have certain theoretical and phenomenological advantages over their continuous counterparts. This paper deals with one-dimensional discretizations and examines the extent to which dynamical metastability, which manifests itself in the original partial di...
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Stability analyses and error estimates are carried out for a number of commonly used numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the schemes we considered are either unconditionally energy stable, or conditionally energy stable with reasonable stability conditions in the semi-discretized versions. Error estimates for selected schemes with a spectral-Ga...
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Long time asymptotics are developed here for an Allen-Cahn/Cahn-Hilliard system derived recently by Cahn & Novick-Cohen [11] as a di use interface model for simultaneous orderdisorder and phase separation. Proximity to a deep quench limit is assumed, and spatial scales are chosen to model Krzanowski instabilities in which droplets of a minor disordered phase bounded by interphase boundaries (IP...
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A fully computable upper bound for the finite element approximation error of Allen– Cahn and Cahn–Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element me...
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Article history: Received 10 May 2013 Received in revised form 18 July 2014 Accepted 2 August 2014 Available online 8 August 2014
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 1995
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/8/5/012