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

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


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