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On convergence rate of finite element eigenvalue analysis with mass lumping by nodal quadrature

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Abstract

Error bounds are obtained for the finite element eigenvalue analysis using the diagonal mass matrix lumped by nodal quadrature. Finite element results of various two-dimensional 2nd order eigenvalue problems and a one-dimensional 4th order eigenvalue problem are compared favorably with the theoretical predictions. Estimates of error bounds, particularly those for eigenvalues, are significantly improved over the existing results, and their range of applicability is broadened. Special attention has been focused on the cases where shape functions have incomplete polynomials.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Akron, 44325, Akron, OH, USA

    Y. -N. Li

  2. Department of Mechanics, Peking University, Bejing, Peoples Republic of China

    R. Y. Liang & D. -J. Wang

Authors
  1. Y. -N. Li
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  2. R. Y. Liang
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  3. D. -J. Wang
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Communicated by S. N. Atluri, March 20, 1991

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Li, Y.N., Liang, R.Y. & Wang, D.J. On convergence rate of finite element eigenvalue analysis with mass lumping by nodal quadrature. Computational Mechanics 8, 249–256 (1991). https://doi.org/10.1007/BF00577378

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  • DOI: https://doi.org/10.1007/BF00577378

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