TY - JOUR

T1 - Numerical Approximation of a Reaction-Diffusion System with Fast Reversible Reaction

AU - Eymard, Robert

AU - Hilhorst, Danielle

AU - Murakawa, Hideki

AU - Olech, Michal

N1 - Funding Information:
Manuscript received May 29, 2010. Published online August 25, 2010. ∗UniversitéParis-Est, 77454 Marne-la-Vallée Cedex 2, France. E-mail: Robert.Eymard@univ-mlv.fr ∗∗Laboratoire de Mathématiques, CNRS and Universitéde Paris-Sud 11, 91405 Orsay Cédex, France. E-mail: Danielle.Hilhorst@math.u-psud.fr ∗∗∗Graduate School of Science and Engineering for Research, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan. E-mail: murakawa@sci.u-toyama.ac.jp ∗∗∗∗Instytut Matematyczny Uniwersytetu Wroclawskiego, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Polska; Laboratoire de Mathématiques, CNRS Université de Paris-Sud, 91405 Orsay Cédex, France. E-mail: olech@math.uni.wroc.pl ∗∗∗∗∗Project supported by a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Programme (No. MTKD-CT-2004-013389).

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.1007/s11401-010-0604-5

DO - 10.1007/s11401-010-0604-5

M3 - Article

AN - SCOPUS:77957891933

SN - 0252-9599

VL - 31

SP - 631

EP - 654

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 5

ER -