Stability analysis of mixed finite element formulations with special mention of equal‐order interpolations

Published in Int. J. Numer. Meth. Fluids Vol. 20 (8-9), pp. 1003-1022, 1995
doi: 10.1002/fld.1650200819

Abstract

We present a method to assess the stability of pairs of interpolation spaces for mixed formulations. The method is based on a straightforward calculation of the eigenvalues of the discrete matrices through Fourier decomposition in plane waves and is intended to give, via straightforward numerical computations, a sharper determination of stability than the well‐known ‘patch test’ of Zienkiewicz et al. Special attention is devoted to the study of stability and accuracy of equal‐order interpolations.