Analysis of classical and spectral finite element spatial discretization in one-dimensional elastic wave propagation

Abstract eng:
The spatial discretization of continuum by finite element method introduces the dispersion error to numerical solutions of stress wave propagation. For higher order finite elements there are the optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefront. In seismology the spectral finite elements appeared recently. Spectral finite elements are of h-type finite elements, where nodes have special positions along the elements corresponding to the numerical quadrature schemes, but the displacements along element are approximated by Lagrangian interpolation polynomials. The Legendre higher order spectral elements are popular due to their small dispersion and anisotropy errors. In this paper, the classical and Legendre and Chebyshev spectral finite elements are tested in one-dimensional wave propagation in an elastic bar.

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