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Least-squares Galerkin procedure for second-order hyperbolic equations

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Abstract

This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in (L 2(Ω))2 × L 2(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, China University of Petroleum, Dongying, 257061, China

    Hui Guo

  2. School of Mathematics and System Science, Shandong University, Jinan, 250100, China

    Hongxing Rui

  3. Network and Education Technology Center, China University of Petroleum, Dongying, 257061, China

    Chao Lin

Authors
  1. Hui Guo
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  2. Hongxing Rui
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  3. Chao Lin
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Corresponding author

Correspondence to Hui Guo.

Additional information

This research is supported by the Mathematical Tianyuan Foundation of China under Grant No. 10726032, the National Natural Science Foundation of China under Grant No. 10471099, and the Fundamental Research Funds for the Central Universities.

This paper was recommended for publication by Editor Ningning YAN.

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Guo, H., Rui, H. & Lin, C. Least-squares Galerkin procedure for second-order hyperbolic equations. J Syst Sci Complex 24, 381–393 (2011). https://doi.org/10.1007/s11424-010-8015-y

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  • DOI: https://doi.org/10.1007/s11424-010-8015-y

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