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| Numerical Approximation of a Reaction-Diffusion System with Fast Reversible Reaction |
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Citation： |
Robert EYMARD,Danielle HILHORST,Hideki MURAKAWA,Michal OLECH.Numerical Approximation of a Reaction-Diffusion System with Fast Reversible Reaction[J].Chinese Annals of Mathematics B,2010,31(5):631~654 |
| Page view： 1780
Net amount： 1186 |
Authors： |
Robert EYMARD; Danielle HILHORST; Hideki MURAKAWA; Michal OLECH; |
Foundation： |
a Marie Curie Transfer of Knowledge Fellowship of the European Community’s
Sixth Framework Programme (No. MTKD-CT-2004-013389). |
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| 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 |
Classification： |
35K45, 35K50, 35K55, 65M12, 65N12, 65N22,
80A30, 92E20 |
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