EIGENVALUES OF BLOCK MATRICES ARISING FROM PROBLEMS IN FLUID-MECHANICS

Block matrices with a special structure arise from mixed finite elemen t discretizations of incompressible flow problems. This paper is conce rned with an analysis of the eigenvalue problem for such matrices and the derivation of two shifted eigenvalue problems that are more suited to numerical solution by iterative algorithms like simultaneous itera tion and Arnoldi's method. The application of the shifted eigenvalue p roblems to the determination of the eigenvalue of smallest real part i s discussed and a numerical example arising from a stability analysis of double-diffusive convection is described.