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Mathematical analysis of a structure-preserving approximation of the bidimensional vorticity equation

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Summary

We show the consistency and the convergence of a spectral approximation of the bidimensional vorticity equation, proposed by V. Zeitlin in[13] and studied numerically by I. Szunyogh, B. Kadar, and D. Dévényi in [12], whose main feature is that it preserves the Hamiltonian structure of the vorticity equation.

Résumé

On démontre la consistance et la convergence d'une approximation spectrale de l'équation du tourbillon bidimensionnelle périodique, proposée par V. Zeitlin dans [13] et étudiée numériquement par I. Szunyogh, B. Kadar et D. Dévényi dans [12]; sa caractéristique principale est de préserver la structure hamiltonienne de l'équation du tourbillon.

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Received February 22, 2000 / Revised version received October 23, 2000 / Published online June 20, 2001

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Gallagher, I. Mathematical analysis of a structure-preserving approximation of the bidimensional vorticity equation. Numer. Math. 91, 223–236 (2002). https://doi.org/10.1007/s002110100293

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  • DOI: https://doi.org/10.1007/s002110100293

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