On eigenvalue approximations by mixed finite element methods

The error analysis for the abstract eigenvalue problem is applied to various examples to illustrate the theory. The first example is the energy stability of incompressible viscous flows while the second example is an acoustic eigenvalue problem for a fluid with a variable speed of sound which is contained in an enclosure. An additional example is analyzed to illustrate the nonselfadjoint aspect of the theory. In each of the examples the solution is approximated by mixed finite element methods which ultimately leads to a linear generalized eigenvalue problem to be solved. Numerical results for each example are presented which illustrate the abstract error estimate.