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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.
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Dept of Mathematics Research Papers
Mathematical Sciences

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