✦ LIBER ✦

Two-grid methods for mixed finite-element solution of coupled reaction-diffusion systems

✍ Scribed by Li Wu; Myron B. Allen

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 423 KB
Volume: 15
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199909)15:5<589::aid-num6>3.0.co;2-w

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✦ Synopsis

We develop 2-grid schemes for solving nonlinear reaction-diffusion systems:

where p = (p, q) is an unknown vector-valued function. The schemes use discretizations based on a mixed finite-element method. The 2-grid approach yields iterative procedures for solving the nonlinear discrete equations. The idea is to relegate all the Newton-like iterations to grids much coarser than the final one, with no loss in order of accuracy. The iterative algorithms examined here extend a method developed earlier for single reaction-diffusion equations. An application to prepattern formation in mathematical biology illustrates the method's effectiveness.

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