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A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients

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Abstract

We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear system is solved by the preconditioned conjugate gradient (PCG) method with a preconditioner which is shown to be spectrally equivalent to the matrix of the resulting linear system. Numerical tests demonstrating the convergence properties of the scheme and PCG are presented.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80401-1887, USA

    Bernard Bialecki

  2. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    Andreas Karageorghis

Authors
  1. Bernard Bialecki
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  2. Andreas Karageorghis
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Correspondence to Andreas Karageorghis.

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Bialecki, B., Karageorghis, A. A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients. Numer Algor 77, 491–516 (2018). https://doi.org/10.1007/s11075-017-0325-x

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  • DOI: https://doi.org/10.1007/s11075-017-0325-x

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