Errors due to spatial discretization and numerical precision in the finite-element method

The effects of the spatial discretization and the numerical precision on a plane wave propagating through a finite-element mesh are investigated in this work. The spatial discretization results in dispersion in the amplitude and the phase of the wave and in a non-uniform rate of convergence within an element. The finite precision in the calculations used in a finite-element code results in degraded accuracy. These errors are investigated as a function of the node density, the order of the elements, and the precision of the calculations used in the finite element code. The errors for first- through eighth-order elements are investigated both analytically and numerically.<
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