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摘要
This paper concerns a second-order, three level piecewise linear finite element scheme 2-SBDF (Ruuth, in J Math Biol 34:148-176, 1995) for approximating the stationary (Turing) patterns of a well-known experimental substrate-inhibition reaction-diffusion (%26apos;Thomas%26apos;) system (Thomas, in Analysis and control of immobilized enzyme systems, pp 115-150, 1975). A numerical analysis of the semi-discrete in time approximations leads to semi-discrete a priori bounds and an optimal error estimate. The analysis highlights the technical challenges in undertaking the numerical analysis of multi-level () schemes. We illustrate the effectiveness of the numerical method by repeating an important classical experiment in mathematical biology, namely, to approximate the Turing patterns of the Thomas system over a schematic mammal skin domain with fixed geometry at various scales. We also make some comments on the correct procedure for simulating Turing patterns in general reaction-diffusion systems.
- 出版日期2014-7
