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

Abstract

We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce 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 chemical kinetics factor. 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.

22 pages, 6 figures, packages used: amsmath, amssymb, mathrsfs, nicefrac, graphicx, amsthm