The solution of elastostatic and elastodynamic problems with Chebyshev spectral finite elements

Chebyshev spectral finite elements are applied to the solution of elastostatic and elastodynamic problems in two dimensions. The accuracy of the spectral approach is judged by examining the dispersion of the solutions. It is shown that the spectral approach can achieve nearly zero dispersion for a wide range of spatial and temporal discretizations. Even coarse mesh solutions using the explicit lumped capacitance approach demonstrate exceptional accuracy. A brief description of the development of the Chebyshev spectral elements is included.

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