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Mixed finite element methods for the Rosenau equation

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Abstract

Mixed finite element methods are applied to the Rosenau equation by employing splitting technique. The semi-discrete methods are derived using \(C^0-\)piecewise linear finite elements in spatial direction. The existence of unique solutions of the semi-discrete and fully discrete Galerkin mixed finite element methods is proved, and error estimates are established in one space dimension. An extension to problem in two space variables is also discussed. It is shown that the Galerkin mixed finite finite element have the same rate of convergence as in the classical methods without requiring the LBB consistency condition. At last numerical experiments are carried out to support the theoretical claims.

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Authors and Affiliations

  1. Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, 4003, Sousse Ibn Khaldoun, Tunisia

    Noureddine Atouani, Yousra Ouali & Khaled Omrani

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  1. Noureddine Atouani
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  2. Yousra Ouali
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  3. Khaled Omrani
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Correspondence to Khaled Omrani.

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Atouani, N., Ouali, Y. & Omrani, K. Mixed finite element methods for the Rosenau equation. J. Appl. Math. Comput. 57, 393–420 (2018). https://doi.org/10.1007/s12190-017-1112-5

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  • DOI: https://doi.org/10.1007/s12190-017-1112-5

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