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An \(H^{1}-\)Galerkin mixed finite element method for rosenau equation

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Abstract

In this paper, by applying a splitting technique, the non-linear fourth order Rosenau equation is split into a system of coupled equations. Then, an \(H^{1}-\) Galerkin mixed finite element method is proposed for the resultant equations after employing a suitable weak formulation. Semi-discrete and fully discrete schemes are discussed and respective optimal order error estimates are obtained without any constraints on the mesh. Finally, numerical results are computed to validate the efficacy of the method. The proposed method has advantages in respect of higher order error estimate, less requirement of regularity on exact solution and also with reduced size i.e. less than half of the size of resulting linear system over that of mentioned in Manickam et al. (Numer Methods Partial Differ Equ (14):695–716, 1998).

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Authors and Affiliations

  1. Deparment of Mathematics, Anna University, CEG Campus, Guindy, Chennai, 600025, India

    L. Jones Tarcius Doss & L. Aishwarya

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  1. L. Jones Tarcius Doss
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  2. L. Aishwarya
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Correspondence to L. Jones Tarcius Doss.

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Communicated by Frederic Valentin.

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Doss, L.J.T., Aishwarya, L. An \(H^{1}-\)Galerkin mixed finite element method for rosenau equation. Comp. Appl. Math. 42, 112 (2023). https://doi.org/10.1007/s40314-023-02255-4

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  • DOI: https://doi.org/10.1007/s40314-023-02255-4

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