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Error estimates of spectral Legendre–Galerkin methods for the fourth-order equation in one dimension

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  • Chen, Yanping
  • Zhou, Jianwei

Abstract

We employ spectral Legendre–Galerkin and mixed Legendre–Galerkin approximations to solve the first bi-harmonic equation in one dimension, respectively. By orthogonal properties of Legendre polynomials, we obtain an explicit a posteriori error indicator for spectral Legendre–Galerkin methods. Furthermore, in virtue of an auxiliary variable, we present spectral mixed Legendre–Galerkin methods and study the a priori estimate and a posteriori error indicator. Especially, these indicators only depend on the expansions of the right-hand item. Numerical examples are presented to verify our theoretical analysis.

Suggested Citation

  • Chen, Yanping & Zhou, Jianwei, 2015. "Error estimates of spectral Legendre–Galerkin methods for the fourth-order equation in one dimension," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1217-1226.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:1217-1226
    DOI: 10.1016/j.amc.2015.06.082
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    Cited by:

    1. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.

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