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H1-Galerkin Mixed Finite Element Method for the Regularized Long Wave Equation

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Abstract

In this paper, an H1-Galerkin mixed finite element method is proposed for the 1-D regularized long wave (RLW) equation u t +u x +uu x −δu xxt =0. The existence of unique solutions of the semi-discrete and fully discrete H1-Galerkin mixed finite element methods is proved, and optimal error estimates are established. Our method can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Shanghai Jiao Tong University, Dongchuan Road, Shanghai, 200240, China

    L. Guo

  2. Department of Mathematics, Shandong Normal University, East of Wenhua Road, Jinan, China

    H. Chen

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  1. L. Guo
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  2. H. Chen
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Correspondence to L. Guo.

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Guo, L., Chen, H. H1-Galerkin Mixed Finite Element Method for the Regularized Long Wave Equation. Computing 77, 205–221 (2006). https://doi.org/10.1007/s00607-005-0158-7

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  • DOI: https://doi.org/10.1007/s00607-005-0158-7

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