Abstract
AbstractIn static force‐deflection applications of the finite element method, convergence rates for the p‐version, in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed, are superior to those for the h‐version, in which the element degree remains fixed while the mesh is refined so that element size approaches zero. In structural dynamics applications, one does not seek to approximate a single solution, as in static applications, but seeks estimates for a number of the lower system eigenvalues. This paper identifies factors responsible for poorer accuracy in higher computed eigenvalues. In addition, it explains why the p‐version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h‐version. Numerical examples demonstrate the superiority of the p‐version over the h‐version. They also show the effects of various mechanisms limiting eigenvalue convergence.
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