Eigenvalue convergence in the finite element method

In 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.