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Pré-Publication, Document De Travail Année : 2009

Analysis of a fractional-step scheme for the P1 radiative diffusion model

Résumé

We address in this paper a nonlinear parabolic system, which is built to retain the main mathematical difficulties of the P1 radiative diffusion physical model. We propose a finite volume fractional-step scheme for this problem enjoying the following properties. First, we show that each discrete solution satisfies a priori L -estimates, through a discrete maxi- mum principle; by a topological degree argument, this yields the existence of a solution, which is proven to be unique. Second, we establish uniform (with respect to the size of the meshes and the time step) L2 -bounds for the space and time translates; this proves, by the Kolmogorov theorem, the relative compactness of any sequence of solutions obtained through a sequence of discretizations the time and space steps of which tend to zero; the limits of converging subsequences are then shown to be a solution to the continuous problem. Estimates of time translates of the discrete solutions are obtained through the formalization of a generic argument, interesting for its own sake.
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Dates et versions

hal-00477086 , version 1 (28-04-2010)
hal-00477086 , version 2 (02-03-2017)

Identifiants

  • HAL Id : hal-00477086 , version 1

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Raphaele Herbin, Thierry Gallouët, Jean-Claude Latché, Aurélien Larcher. Analysis of a fractional-step scheme for the P1 radiative diffusion model. 2009. ⟨hal-00477086v1⟩
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