Numerical approximation of a reaction-diffusion system with fast reversible reaction

Abstract

The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate. It follows that the solution converges to the solution of a nonlinear diffusion problem, as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.

Keywords

Instantaneous reaction limit / Mass-action kinetics / Finite volume methods / Convergence of approximate solutions / Discrete a priori estimates / Kolmogorov’s theorem

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