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A reaction-diffusion system of \(\lambda-\omega\) type. II: Numerical analysis. (English) Zbl 1160.35439
Summary: We undertake the numerical analysis of a reaction-diffusion system of ‘\(\lambda-\omega\)’ type [N. Kopell and L. N. Howard, Stud. Appl. Math. 52, 291–328 (1973; Zbl 0305.35081)]. Results are presented for a fully-practical piecewise linear finite element method by mimicking results in the continuous case [cf. Part I, Eur. J. Appl. Math. 16, No. 1, 1–19 (2005; Zbl 1079.35043 )]. We establish a priori estimates and error bounds for a semi-discrete and a fully discrete finite element approximation. The theoretical results are illustrated and verified via the numerical solution of periodic plane waves in one space dimension. Experiments in two space dimensions led to‘target patterns’ and spiral wave break-up.

35K57 Reaction-diffusion equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35B45 A priori estimates in context of PDEs
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