WIAS Preprint No. 1934, (2014)

Uniform estimate of the relative free energy by the dissipation rate for finite volume discretized reaction-diffusion systems



Authors

  • Fiebach, André
  • Glitzky, Annegret

2010 Mathematics Subject Classification

  • 65M08 35B40 35K57 35R05 46E39

Keywords

  • Admissible finite volume mesh, reaction-diffusion system, free energy, discrete Poincare and, Sobolev-Poincare inequality

Abstract

We prove a uniform Poincare-like estimate of the relative free energy by the dissipation rate for implicit Euler, finite volume discretized reaction-diffusion systems. This result is proven indirectly and ensures the exponential decay of the relative free energy with a unified decay rate for admissible finite volume meshes.

Appeared in

  • Finite Volumes for Complex Applications VII -- Methods and Theoretical Aspects -- FVCA 7, Berlin, June 2014, J. Fuhrmann, M. Ohlberger, Ch. Rohde, eds., vol. 77 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2014, pp. 275--283

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