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 -