Compactness of discrete approximate solutions to parabolic PDEs - Application to  a turbulence model

T. Gallouët; J.-C. Latché

doi:10.3934/cpaa.2012.11.2371

Article Contents

2012, Volume 11, Issue 6: 2371-2391. Doi: 10.3934/cpaa.2012.11.2371

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Compactness of discrete approximate solutions to parabolic PDEs - Application to a turbulence model

T. Gallouët^1, and
J.-C. Latché^2,

1.
Université de Provence, CMI, Marseille
2.
Institut de Radioprotection et de Sûret

Received: September 30, 2010

Revised: October 31, 2010

Published: October 2012

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Abstract

In this paper, we prove an adaptation of the classical compactness Aubin-Simon lemma to sequences of functions obtained through a sequence of discretizations of a parabolic problem. The main difficulty tackled here is to generalize the classical proof to handle the dependency of the norms controlling each function $u^{(n)}$ of the sequence with respect to $n$. This compactness result is then used to prove the convergence of a numerical scheme combining finite volumes and finite elements for the solution of a reduced turbulence problem.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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