Stable approximation of the advection-diffusion equation using the invariant measure

Abstract : We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The approach has been summarized in [C. Le Bris, F. Legoll and F. Madiot, C. R. Acad. Sci. Paris, Serie I, vol. 354, 799-803 (2016)]. We show that the approach allows for an unconditionally well-posed finite element approximation. We provide a numerical analysis and a set of comprehensive numerical tests showing that the approach can be stable, as accurate as, and more robust than a classical stabilization approach.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01367417
Contributeur : Frederic Legoll <>
Soumis le : vendredi 16 septembre 2016 - 10:16:10
Dernière modification le : jeudi 14 septembre 2017 - 01:08:56

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  • HAL Id : hal-01367417, version 1
  • ARXIV : 1609.04777

Citation

Claude Le Bris, Frederic Legoll, François Madiot. Stable approximation of the advection-diffusion equation using the invariant measure. 2017. 〈hal-01367417〉

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