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http://bura.brunel.ac.uk/handle/2438/3113
Title: | Finite element approximation of non-Fickian polymer diffusion |
Authors: | Bauermeister, N Shaw, S |
Issue Date: | 2009 |
Publisher: | Oxford University Press |
Series/Report no.: | IMA Journal of Numerical Analysis. In press. |
Abstract: | The problem of nonlinear non-Fickian polymer diffusion as modelled by a diffusion equation with an adjoined spatially local evolution equation for a viscoelastic stress is considered (see, for example, Cohen, White & Witelski, SIAM J. Appl. Math. 55, pp. 348–368, 1995). We present numerical schemes based, spatially, on the Galerkin finite element method and, temporally, on the Crank-Nicolson method. Special attention is paid to linearising the discrete equations by extrapolating the value of the nonlinear term from previous time steps. Optimal a priori error estimates are given, based on the assumption that the exact solution possesses certain regularity properties, and numerical experiments are given to support these error estimates. |
URI: | http://bura.brunel.ac.uk/handle/2438/3113 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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nonfick_norbert_2008.pdf | 1.15 MB | Adobe PDF | View/Open |
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