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.