Discrete spectrum analyses for various mixed discretizations of the Stokes eigenproblem

Abstract

We conduct discrete spectrum analyses for a selection of mixed discretization schemes for the Stokes eigenproblem. In particular, we consider the MINI element, the Crouzeix---Raviart element, the Marker-and-Cell scheme, the Taylor---Hood element, the $${\mathbf{Q}_{k}/P_{k-1}}$$ element, the divergence-conforming discontinuous Galerkin method, and divergence-conforming B-splines. For each of these schemes, we compare the spectrum for the continuous Stokes problem with the spectrum for the discrete Stokes problem, and we discuss the relationship of eigenvalue errors with solution errors associated with unsteady viscous flow problems.