Finite-element approximation of non-Fickian polymer diffusion
نویسندگان
چکیده
منابع مشابه
Finite Element Approximation of a Non-local Problem in Non-fickian Polymer Diffusion
Abstract. The problem of non-local nonlinear non-Fickian polymer diffusion as modelled by a diffusion equation with a nonlinearly coupled boundary value problem for a viscoelastic ‘pseudostress’ is considered (see, for example, DA Edwards in Z. angew. Math. Phys., 52, 2001, pp. 254—288). We present two numerical schemes using the implicit Euler method and also the Crank-Nicolson method. Each sc...
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We consider discrete schemes for a nonlinear model of non-Fickian diffusion in viscoelastic polymers. The model is motivated by, but not the same as, that proposed by Cohen et al. in SIAM J. Appl. Math., 55, pp. 348–368, 1995. The spatial discretisation is effected with both the symmetric and non-symmetric interior penalty discontinuous Galerkin finite element method, and the time discretisatio...
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Diffusion of penetrants through polymers often does not follow the standard Fickian model. Such anomalous behavior can cause difficulty when designing polymer networks for specific uses. One type of non-Fickian behavior that results is so-called case I1 diffusion, where Fickian-like fronts initially move like fi with a transition to a non-Fickian concentration profile and front speed for modera...
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In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behaviour is represented by a Voigt-Kelvin model or a Maxwell model. We propose a finite difference discretization defined on a general nonuniform grid and we show second conv...
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2009
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drn071