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Explicit bound for quadratic Lagrange interpolation constant on triangular finite elements

Author

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  • Liu, Xuefeng
  • You, Chun’guang

Abstract

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the interpolation constant is obtained by solving an eigenvalue problem along with explicit lower bound for its eigenvalues. The lower bound for interpolation constant can be easily obtained by applying the Rayleigh–Ritz method. Numerical computation is performed to demonstrate the sharpness of lower and upper bounds of the interpolation constants over triangles of different shapes. An online computing demo is available at http://www.xfliu.org/onlinelab/.

Suggested Citation

  • Liu, Xuefeng & You, Chun’guang, 2018. "Explicit bound for quadratic Lagrange interpolation constant on triangular finite elements," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 693-701.
    • Handle: RePEc:eee:apmaco:v:319:y:2018:i:c:p:693-701
    DOI: 10.1016/j.amc.2017.08.020
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    References listed on IDEAS

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    1. Liu, Xuefeng, 2015. "A framework of verified eigenvalue bounds for self-adjoint differential operators," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 341-355.
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